Fast EMA above Slow EMA with MACD (by Coinrule)An exponential moving average ( EMA ) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average . An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average simple moving average ( SMA ), which applies an equal weight to all observations in the period.
Moving average convergence divergence ( MACD ) is a trend-following momentum indicator that shows the relationship between two moving averages of a security’s price. The MACD is calculated by subtracting the 26-period exponential moving average ( EMA ) from the 12-period EMA .
The result of that calculation is the MACD line. A nine-day EMA of the MACD called the "signal line," is then plotted on top of the MACD line, which can function as a trigger for buy and sell signals. Traders may buy the coin when the MACD crosses above its signal line and sell—or short—the security when the MACD crosses below the signal line. Moving average convergence divergence ( MACD ) indicators can be interpreted in several ways, but the more common methods are crossovers, divergences, and rapid rises/falls.
The Strategy enters and closes the trade when the following conditions are met:
LONG
The MACD histogram turns bullish
EMA8 is greater than EMA26
EXIT
Price increases 3% trailing
Price decreases 1% trailing
This strategy is back-tested from 1 January 2022 to simulate how the strategy would work in a bear market and provides good returns.
Pairs that produce very strong results include AXSUSDT on the 5-minute timeframe. This short timeframe means that this strategy opens and closes trades regularly.
Additionally, the trailing stop loss and take profit conditions can also be changed to match your needs.
The strategy assumes each order is using 30% of the available coins to make the results more realistic and to simulate you only ran this strategy on 30% of your holdings. A trading fee of 0.1% is also taken into account and is aligned to the base fee applied on Binance.
Cerca negli script per "Exponential"
oussamacryptoWhat Is an Exponential Moving Average (EMA)?
An exponential moving average (EMA) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average simple moving average (SMA), which applies an equal weight to all observations in the period.
Indicators Combination Framework v3 IND [DTU]Hello All,
This script is a framework to analyze and see the results by combine selected indicators for (long, short, longexit, shortexit) conditions.
I was designed this for beginners and users to facilitate to see effects of the technical indicators combinations on the chart WITH NO CODE
You can improve your strategies according the results of this system by connecting the framework to a strategy framework/template such as Pinecoder, Benson, daveatt or custom.
This is enhanced version of my previous indicator "Indicators & Conditions Test Framework "
Currently there are 93 indicators (23 newly added) connected over library. You can also import an External Indicator or add Custom indicator (In the source)
It is possible to change it from Indicator to strategy (simple one) by just remarking strategy parts in the source code and see real time profit of your combinations
Feel free to change or use it in your source
Special thanks goes to Pine wizards: Trading view (built-in Indicators), @Rodrigo, @midtownsk8rguy, @Lazybear, @Daveatt and others for their open source codes and contributions
SIMPLE USAGE
1. SETTING: Show Alerts= True (To see your entries and Exists)
2. Define your Indicators (ex: INDICATOR1: ema(close,14), INDICATOR2: ema(close,21), INDICATOR3: ema(close,200)
3. Define Your Combinations for long & Short Conditions
a. For Long: (INDICATOR1 crossover INDICATOR2) AND (INDICATOR3 < close)
b. For Short: (INDICATOR1 crossunder INDICATOR2) AND (INDICATOR3 > close)
4. Select Strategy/template (Import strategy to chart) that you export your signals from the list
5. Analyze the best profit by changing Indicators values
SOME INDICATORS DETAILS
Each Indicator includes:
- Factorization : Converting the selected indicator to Double, triple Quadruple such as EMA to DEMA, TEMA QEMA
- Log : Simple or log10 can be used for calculation on function entries
- Plot Type : You can overlay the indicator on the chart (such ema) or you can use stochastic/Percentrank approach to display in the variable hlines range
- Extended Parametes : You can use default parameters or you can use extended (P1,P2) parameters regarding to indicator type and your choice
- Color : You can define indicator color and line properties
- Smooth : you can enable swma smooth
- indicators : you can select one of the 93 function like ema(),rsi().. to define your indicator
- Source : you can select from already defined indicators (IND1-4), External Indicator (EXT), Custom Indicator (CUST), and other sources (close, open...)
CONDITION DETAILS
- There are are 4 type of conditions, long entry, short entry, long exit, short exit.
- Each condition are built up from 4 combinations that joined with "AND" & "OR" operators
- You can see the results by enabling show alerts check box
- If you only wants to enter long entry and long exit, just fill these conditions
- If "close on opposite" checkbox selected on settings, long entry will be closed on short entry and vice versa
COMBINATIONS DETAILS
- There are 4 combinations that joined with "AND" & "OR" operators for each condition
- combinations are built up from compare 1st entry with 2nd one by using operator
- 1st and 2nd entries includes already defined indicators (IND1-5), External Indicator (EXT), Custom Indicator (CUST), and other sources (close, open...)
- Operators are comparison values such as >,<, crossover,...
- 2nd entry include "VALUE" parameter that will use to compare 1st indicator with value area
- If 2nd indicator selected different than "VALUE", value are will mean previous value of the selection. (ex: value area= 2, 2nd entry=close, means close )
- Selecting "NONE" for the 1st entry will disable calculation of current and following combinations
JOINS DETAILS
- Each combination will join wiht the following one with the JOIN (AND, OR) operator (if the following one is not equal "NONE")
CUSTOM INDICATOR
- Custom Indicator defines harcoded in the source code.
- You can call it with "CUST" in the Indicator definition source or combination entries source
- You can change or implement your custom indicator by updating the source code
EXTERNAL INDICATOR
- You can import an external indicator by selecting it from the ext source.
- External Indicator should be already imported to the chart and it have an plot function to output its signal
EXPORTING SIGNAL
- You can export your result to an already defined strategy template such as Pine coders, Benson, Daveatt Strategy templates
- Or you can define your custom export for other future strategy templates
ALERTS
- By enabling show alerts checkbox, you can see long entry exits on the bottom, and short entry exits aon the top of the chart
ADDITIONAL INFO
- You can see all off the inputs descriptions in the tooltips. (You can also see the previous version for details)
- Availability to set start, end dates
- Minimize repainting by using security function options (Secure, Semi Secure, Repaint)
- Availability of use timeframes
-
Version 3 INDICATORS LIST (More to be added):
▼▼▼ OVERLAY INDICATORS ▼▼▼
alma(src,len,offset=0.85,sigma=6).-------Arnaud Legoux Moving Average
ama(src,len,fast=14,slow=100).-----------Adjusted Moving Average
accdist().-------------------------------Accumulation/distribution index.
cma(src,len).----------------------------Corrective Moving average
dema(src,len).---------------------------Double EMA (Same as EMA with 2 factor)
ema(src,len).----------------------------Exponential Moving Average
gmma(src,len).---------------------------Geometric Mean Moving Average
highest(src,len).------------------------Highest value for a given number of bars back.
hl2ma(src,len).--------------------------higest lowest moving average
hma(src,len).----------------------------Hull Moving Average.
lagAdapt(src,len,perclen=5,fperc=50).----Ehlers Adaptive Laguerre filter
lagAdaptV(src,len,perclen=5,fperc=50).---Ehlers Adaptive Laguerre filter variation
laguerre(src,len).-----------------------Ehlers Laguerre filter
lesrcp(src,len).-------------------------lowest exponential esrcpanding moving line
lexp(src,len).---------------------------lowest exponential expanding moving line
linreg(src,len,loffset=1).---------------Linear regression
lowest(src,len).-------------------------Lovest value for a given number of bars back.
mcginley(src, len.-----------------------McGinley Dynamic adjusts for market speed shifts, which sets it apart from other moving averages, in addition to providing clear moving average lines
percntl(src,len).------------------------percentile nearest rank. Calculates percentile using method of Nearest Rank.
percntli(src,len).-----------------------percentile linear interpolation. Calculates percentile using method of linear interpolation between the two nearest ranks.
previous(src,len).-----------------------Previous n (len) value of the source
pivothigh(src,BarsLeft=len,BarsRight=2).-Previous pivot high. src=src, BarsLeft=len, BarsRight=p1=2
pivotlow(src,BarsLeft=len,BarsRight=2).--Previous pivot low. src=src, BarsLeft=len, BarsRight=p1=2
rema(src,len).---------------------------Range EMA (REMA)
rma(src,len).----------------------------Moving average used in RSI. It is the exponentially weighted moving average with alpha = 1 / length.
sar(start=len, inc=0.02, max=0.02).------Parabolic SAR (parabolic stop and reverse) is a method to find potential reversals in the market price direction of traded goods.start=len, inc=p1, max=p2. ex: sar(0.02, 0.02, 0.02)
sma(src,len).----------------------------Smoothed Moving Average
smma(src,len).---------------------------Smoothed Moving Average
super2(src,len).-------------------------Ehlers super smoother, 2 pole
super3(src,len).-------------------------Ehlers super smoother, 3 pole
supertrend(src,len,period=3).------------Supertrend indicator
swma(src,len).---------------------------Sine-Weighted Moving Average
tema(src,len).---------------------------Triple EMA (Same as EMA with 3 factor)
tma(src,len).----------------------------Triangular Moving Average
vida(src,len).---------------------------Variable Index Dynamic Average
vwma(src,len).---------------------------Volume Weigted Moving Average
volstop(src,len,atrfactor=2).------------Volatility Stop is a technical indicator that is used by traders to help place effective stop-losses. atrfactor=p1
wma(src,len).----------------------------Weigted Moving Average
vwap(src_).------------------------------Volume Weighted Average Price (VWAP) is used to measure the average price weighted by volume
▼▼▼ NON OVERLAY INDICATORS ▼▼
adx(dilen=len, adxlen=14, adxtype=0).----adx. The Average Directional Index (ADX) is a used to determine the strength of a trend. len=>dilen, p1=adxlen (default=14), p2=adxtype 0:ADX, 1:+DI, 2:-DI (def:0)
angle(src,len).--------------------------angle of the series (Use its Input as another indicator output)
aroon(len,dir=0).------------------------aroon indicator. Aroons major function is to identify new trends as they happen.p1 = dir: 0=mid (default), 1=upper, 2=lower
atr(src,len).----------------------------average true range. RMA of true range.
awesome(fast=len=5,slow=34,type=0).------Awesome Oscilator is an indicator used to measure market momentum. defaults : fast=len= 5, p1=slow=34, p2=type: 0=Awesome, 1=difference
bbr(src,len,mult=1).---------------------bollinger %%
bbw(src,len,mult=2).---------------------Bollinger Bands Width. The Bollinger Band Width is the difference between the upper and the lower Bollinger Bands divided by the middle band.
cci(src,len).----------------------------commodity channel index
cctbbo(src,len).-------------------------CCT Bollinger Band Oscilator
change(src,len).-------------------------A.K.A. Momentum. Difference between current value and previous, source - source . is most commonly referred to as a rate and measures the acceleration of the price and/or volume of a security
cmf(len=20).-----------------------------Chaikin Money Flow Indicator used to measure Money Flow Volume over a set period of time. Default use is len=20
cmo(src,len).----------------------------Chande Momentum Oscillator. Calculates the difference between the sum of recent gains and the sum of recent losses and then divides the result by the sum of all price movement over the same period.
cog(src,len).----------------------------The cog (center of gravity) is an indicator based on statistics and the Fibonacci golden ratio.
copcurve(src,len).-----------------------Coppock Curve. was originally developed by Edwin Sedge Coppock (Barrons Magazine, October 1962).
correl(src,len).-------------------------Correlation coefficient. Describes the degree to which two series tend to deviate from their ta.sma values.
count(src,len).--------------------------green avg - red avg
cti(src,len).----------------------------Ehler s Correlation Trend Indicator by
dev(src,len).----------------------------ta.dev() Measure of difference between the series and its ta.sma
dpo(len).--------------------------------Detrended Price OScilator is used to remove trend from price.
efi(len).--------------------------------Elders Force Index (EFI) measures the power behind a price movement using price and volume.
eom(len=14,div=10000).-------------------Ease of Movement.It is designed to measure the relationship between price and volume.p1 = div: 10000= (default)
falling(src,len).------------------------ta.falling() Test if the `source` series is now falling for `length` bars long. (Use its Input as another indicator output)
fisher(len).-----------------------------Fisher Transform is a technical indicator that converts price to Gaussian normal distribution and signals when prices move significantly by referencing recent price data
histvol(len).----------------------------Historical volatility is a statistical measure used to analyze the general dispersion of security or market index returns for a specified period of time.
kcr(src,len,mult=2).---------------------Keltner Channels Range
kcw(src,len,mult=2).---------------------ta.kcw(). Keltner Channels Width. The Keltner Channels Width is the difference between the upper and the lower Keltner Channels divided by the middle channel.
klinger(type=len).-----------------------Klinger oscillator aims to identify money flow’s long-term trend. type=len: 0:Oscilator 1:signal
macd(src,len).---------------------------MACD (Moving Average Convergence/Divergence)
mfi(src,len).----------------------------Money Flow Index s a tool used for measuring buying and selling pressure
msi(len=10).-----------------------------Mass Index (def=10) is used to examine the differences between high and low stock prices over a specific period of time
nvi().-----------------------------------Negative Volume Index
obv().-----------------------------------On Balance Volume
pvi().-----------------------------------Positive Volume Index
pvt().-----------------------------------Price Volume Trend
ranges(src,upper=len, lower=-5).---------ranges of the source. src=src, upper=len, v1:lower=upper . returns: -1 source=upper otherwise 0
rising(src,len).-------------------------ta.rising() Test if the `source` series is now rising for `length` bars long. (Use its Input as another indicator output)
roc(src,len).----------------------------Rate of Change
rsi(src,len).----------------------------Relative strength Index
rvi(src,len).----------------------------The Relative Volatility Index (RVI) is calculated much like the RSI, although it uses high and low price standard deviation instead of the RSI’s method of absolute change in price.
smi_osc(src,len,fast=5, slow=34).--------smi Oscillator
smi_sig(src,len,fast=5, slow=34).--------smi Signal
stc(src,len,fast=23,slow=50).------------Schaff Trend Cycle (STC) detects up and down trends long before the MACD. Code imported from
stdev(src,len).--------------------------Standart deviation
trix(src,len) .--------------------------the rate of change of a triple exponentially smoothed moving average.
tsi(src,len).----------------------------The True Strength Index indicator is a momentum oscillator designed to detect, confirm or visualize the strength of a trend.
ultimateOsc(len.-------------------------Ultimate Oscillator indicator (UO) indicator is a technical analysis tool used to measure momentum across three varying timeframes
variance(src,len).-----------------------ta.variance(). Variance is the expectation of the squared deviation of a series from its mean (ta.sma), and it informally measures how far a set of numbers are spread out from their mean.
willprc(src,len).------------------------Williams %R
wad().-----------------------------------Williams Accumulation/Distribution.
wvad().----------------------------------Williams Variable Accumulation/Distribution.
HISTORY
v3.01
ADD: 23 new indicators added to indicators list from the library. Current Total number of Indicators are 93. (to be continued to adding)
ADD: 2 more Parameters (P1,P2) for indicator calculation added. Par:(Use Defaults) uses only indicator(Source, Length) with library's default parameters. Par:(Use Extra Parameters P1,P2) use indicator(Source,Length,p1,p2) with additional parameters if indicator needs.
ADD: log calculation (simple, log10) option added on indicator function entries
ADD: New Output Signals added for compatibility on exporting condition signals to different Strategy templates.
ADD: Alerts Added according to conditions results
UPD: Indicator source inputs now display with indicators descriptions
UPD: Most off the source code rearranged and some functions moved to the new library. Now system work like a little bit frontend/backend
UPD: Performance improvement made on factorization and other source code
UPD: Input GUI rearranged
UPD: Tooltips corrected
REM: Extended indicators removed
UPD: IND1-IND4 added to indicator data source. Now it is possible to create new indicators with the previously defined indicators value. ex: IND1=ema(close,14) and IND2=rsi(IND1,20) means IND2=rsi(ema(close,14),20)
UPD: Custom Indicator (CUST) added to indicator data source and Combination Indicator source.
UPD: Volume added to indicator data source and Combination Indicator source.
REM: Custom indicators removed and only one custom indicator left
REM: Plot Type "Org. Range (-1,1)" removed
UPD: angle, rising, falling type operators moved to indicator library
Indicator Functions with Factor and HeikinAshiHello all,
This indicator returns below selected indicators values with entered parameters.
Also you can add factorization, functions candles, function HeikinAshi and more to the plot.
VERSION:
Version 1: returns series only source and Length with already defined default values
Version 2: returns series with source, Length, p1 and p2 parameters according to the indicator definition (ex: )
PARAMETERS p1 p2
for defining multi arguments (See indicators list) indicator input value usable with verison=V2 selected.. ex: for alma( src , len ,offset=0.85,sigma=6), set source=source, len=length, p1=0.85 an p2=6
FACTOR:
Add double triple, Quadruple factors to selected indicator (like converting EMA to 2-DEMA, 3-TEMA, 4-QEMA...)
1-Original
2-Double
3-Triple
4-Quadruple
LOG
Log: Use log, log10 on function entries
PLOTTING:
PType: Plotting type of the function on the screen
Original :use original values
Org. Range (-1,1): usable for indicators between range -1 and 1
Stochastic: Convert indicator values by using stochastic calculation between -1 & 1. (use AT/% length to better view)
PercentRank: Convert indicator values by using Percent Rank calculation between -1 & 1. (use AT/% length to better view)
ST/%: length for plotting Type for stochastic and Percent Rank options
Smooth: Use SWMA for smoothing the function
DISPLAY TYPES
Plot Candles: Display the selected indicator as candle by implementing values
Plot Ind: Display result of indicator with selected source
HeikinAshi: Display Selected indicator candles with Heikin Ashi calculation
INDICATOR LIST:
hide = 'DONT DISPLAY', //Dont display & calculate the indicator. (For my framework usage)
alma = 'alma( src , len ,offset=0.85,sigma=6)', // Arnaud Legoux Moving Average
ama = 'ama( src , len ,fast=14,slow=100)', //Adjusted Moving Average
acdst = 'accdist()', // Accumulation/distribution index.
cma = 'cma( src , len )', //Corrective Moving average
dema = 'dema( src , len )', // Double EMA (Same as EMA with 2 factor)
ema = 'ema( src , len )', // Exponential Moving Average
gmma = 'gmma( src , len )', //Geometric Mean Moving Average
hghst = 'highest( src , len )', //Highest value for a given number of bars back.
hl2ma = 'hl2ma( src , len )', //higest lowest moving average
hma = 'hma( src , len )', // Hull Moving Average .
lgAdt = 'lagAdapt( src , len ,perclen=5,fperc=50)', //Ehler's Adaptive Laguerre filter
lgAdV = 'lagAdaptV( src , len ,perclen=5,fperc=50)', //Ehler's Adaptive Laguerre filter variation
lguer = 'laguerre( src , len )', //Ehler's Laguerre filter
lsrcp = 'lesrcp( src , len )', //lowest exponential esrcpanding moving line
lexp = 'lexp( src , len )', //lowest exponential expanding moving line
linrg = 'linreg( src , len ,loffset=1)', // Linear regression
lowst = 'lowest( src , len )', //Lovest value for a given number of bars back.
pcnl = 'percntl( src , len )', //percentile nearest rank. Calculates percentile using method of Nearest Rank.
pcnli = 'percntli( src , len )', //percentile linear interpolation. Calculates percentile using method of linear interpolation between the two nearest ranks.
rema = 'rema( src , len )', //Range EMA (REMA)
rma = 'rma( src , len )', //Moving average used in RSI . It is the exponentially weighted moving average with alpha = 1 / length.
sma = 'sma( src , len )', // Smoothed Moving Average
smma = 'smma( src , len )', // Smoothed Moving Average
supr2 = 'super2( src , len )', //Ehler's super smoother, 2 pole
supr3 = 'super3( src , len )', //Ehler's super smoother, 3 pole
strnd = 'supertrend( src , len ,period=3)', //Supertrend indicator
swma = 'swma( src , len )', //Sine-Weighted Moving Average
tema = 'tema( src , len )', // Triple EMA (Same as EMA with 3 factor)
tma = 'tma( src , len )', //Triangular Moving Average
vida = 'vida( src , len )', // Variable Index Dynamic Average
vwma = 'vwma( src , len )', // Volume Weigted Moving Average
wma = 'wma( src , len )', //Weigted Moving Average
angle = 'angle( src , len )', //angle of the series (Use its Input as another indicator output)
atr = 'atr( src , len )', // average true range . RMA of true range.
bbr = 'bbr( src , len ,mult=1)', // bollinger %%
bbw = 'bbw( src , len ,mult=2)', // Bollinger Bands Width . The Bollinger Band Width is the difference between the upper and the lower Bollinger Bands divided by the middle band.
cci = 'cci( src , len )', // commodity channel index
cctbb = 'cctbbo( src , len )', // CCT Bollinger Band Oscilator
chng = 'change( src , len )', //Difference between current value and previous, source - source.
cmo = 'cmo( src , len )', // Chande Momentum Oscillator . Calculates the difference between the sum of recent gains and the sum of recent losses and then divides the result by the sum of all price movement over the same period.
cog = 'cog( src , len )', //The cog (center of gravity ) is an indicator based on statistics and the Fibonacci golden ratio.
cpcrv = 'copcurve( src , len )', // Coppock Curve. was originally developed by Edwin "Sedge" Coppock (Barron's Magazine, October 1962).
corrl = 'correl( src , len )', // Correlation coefficient . Describes the degree to which two series tend to deviate from their ta. sma values.
count = 'count( src , len )', //green avg - red avg
dev = 'dev( src , len )', //ta.dev() Measure of difference between the series and it's ta. sma
fall = 'falling( src , len )', //ta.falling() Test if the `source` series is now falling for `length` bars long. (Use its Input as another indicator output)
kcr = 'kcr( src , len ,mult=2)', // Keltner Channels Range
kcw = 'kcw( src , len ,mult=2)', //ta.kcw(). Keltner Channels Width. The Keltner Channels Width is the difference between the upper and the lower Keltner Channels divided by the middle channel.
macd = 'macd( src , len )', // macd
mfi = 'mfi( src , len )', // Money Flow Index
nvi = 'nvi()', // Negative Volume Index
obv = 'obv()', // On Balance Volume
pvi = 'pvi()', // Positive Volume Index
pvt = 'pvt()', // Price Volume Trend
rise = 'rising( src , len )', //ta.rising() Test if the `source` series is now rising for `length` bars long. (Use its Input as another indicator output)
roc = 'roc( src , len )', // Rate of Change
rsi = 'rsi( src , len )', // Relative strength Index
smosc = 'smi_osc( src , len ,fast=5, slow=34)', //smi Oscillator
smsig = 'smi_sig( src , len ,fast=5, slow=34)', //smi Signal
stdev = 'stdev( src , len )', //Standart deviation
trix = 'trix( src , len )' , //the rate of change of a triple exponentially smoothed moving average .
tsi = 'tsi( src , len )', //True Strength Index
vari = 'variance( src , len )', //ta.variance(). Variance is the expectation of the squared deviation of a series from its mean (ta. sma ), and it informally measures how far a set of numbers are spread out from their mean.
wilpc = 'willprc( src , len )', // Williams %R
wad = 'wad()', // Williams Accumulation/Distribution .
wvad = 'wvad()' //Williams Variable Accumulation/Distribution
I will update the indicator list when I will update the library
Thanks to tradingview, @RodrigoKazuma for their open source indicators
lib_Indicators_v2_DTULibrary "lib_Indicators_v2_DTU"
This library functions returns included Moving averages, indicators with factorization, functions candles, function heikinashi and more.
Created it to feed as backend of my indicator/strategy "Indicators & Combinations Framework Advanced v2 " that will be released ASAP.
This is replacement of my previous indicator (lib_indicators_DT)
I will add an indicator example which will use this indicator named as "lib_indicators_v2_DTU example" to help the usage of this library
Additionally library will be updated with more indicators in the future
NOTES:
Indicator functions returns only one series :-(
plotcandle function returns candle series
INDICATOR LIST:
hide = 'DONT DISPLAY', //Dont display & calculate the indicator. (For my framework usage)
alma = 'alma(src,len,offset=0.85,sigma=6)', //Arnaud Legoux Moving Average
ama = 'ama(src,len,fast=14,slow=100)', //Adjusted Moving Average
acdst = 'accdist()', //Accumulation/distribution index.
cma = 'cma(src,len)', //Corrective Moving average
dema = 'dema(src,len)', //Double EMA (Same as EMA with 2 factor)
ema = 'ema(src,len)', //Exponential Moving Average
gmma = 'gmma(src,len)', //Geometric Mean Moving Average
hghst = 'highest(src,len)', //Highest value for a given number of bars back.
hl2ma = 'hl2ma(src,len)', //higest lowest moving average
hma = 'hma(src,len)', //Hull Moving Average.
lgAdt = 'lagAdapt(src,len,perclen=5,fperc=50)', //Ehler's Adaptive Laguerre filter
lgAdV = 'lagAdaptV(src,len,perclen=5,fperc=50)', //Ehler's Adaptive Laguerre filter variation
lguer = 'laguerre(src,len)', //Ehler's Laguerre filter
lsrcp = 'lesrcp(src,len)', //lowest exponential esrcpanding moving line
lexp = 'lexp(src,len)', //lowest exponential expanding moving line
linrg = 'linreg(src,len,loffset=1)', //Linear regression
lowst = 'lowest(src,len)', //Lovest value for a given number of bars back.
pcnl = 'percntl(src,len)', //percentile nearest rank. Calculates percentile using method of Nearest Rank.
pcnli = 'percntli(src,len)', //percentile linear interpolation. Calculates percentile using method of linear interpolation between the two nearest ranks.
rema = 'rema(src,len)', //Range EMA (REMA)
rma = 'rma(src,len)', //Moving average used in RSI. It is the exponentially weighted moving average with alpha = 1 / length.
sma = 'sma(src,len)', //Smoothed Moving Average
smma = 'smma(src,len)', //Smoothed Moving Average
supr2 = 'super2(src,len)', //Ehler's super smoother, 2 pole
supr3 = 'super3(src,len)', //Ehler's super smoother, 3 pole
strnd = 'supertrend(src,len,period=3)', //Supertrend indicator
swma = 'swma(src,len)', //Sine-Weighted Moving Average
tema = 'tema(src,len)', //Triple EMA (Same as EMA with 3 factor)
tma = 'tma(src,len)', //Triangular Moving Average
vida = 'vida(src,len)', //Variable Index Dynamic Average
vwma = 'vwma(src,len)', //Volume Weigted Moving Average
wma = 'wma(src,len)', //Weigted Moving Average
angle = 'angle(src,len)', //angle of the series (Use its Input as another indicator output)
atr = 'atr(src,len)', //average true range. RMA of true range.
bbr = 'bbr(src,len,mult=1)', //bollinger %%
bbw = 'bbw(src,len,mult=2)', //Bollinger Bands Width. The Bollinger Band Width is the difference between the upper and the lower Bollinger Bands divided by the middle band.
cci = 'cci(src,len)', //commodity channel index
cctbb = 'cctbbo(src,len)', //CCT Bollinger Band Oscilator
chng = 'change(src,len)', //Difference between current value and previous, source - source .
cmo = 'cmo(src,len)', //Chande Momentum Oscillator. Calculates the difference between the sum of recent gains and the sum of recent losses and then divides the result by the sum of all price movement over the same period.
cog = 'cog(src,len)', //The cog (center of gravity) is an indicator based on statistics and the Fibonacci golden ratio.
cpcrv = 'copcurve(src,len)', //Coppock Curve. was originally developed by Edwin "Sedge" Coppock (Barron's Magazine, October 1962).
corrl = 'correl(src,len)', //Correlation coefficient. Describes the degree to which two series tend to deviate from their ta.sma values.
count = 'count(src,len)', //green avg - red avg
dev = 'dev(src,len)', //ta.dev() Measure of difference between the series and it's ta.sma
fall = 'falling(src,len)', //ta.falling() Test if the `source` series is now falling for `length` bars long. (Use its Input as another indicator output)
kcr = 'kcr(src,len,mult=2)', //Keltner Channels Range
kcw = 'kcw(src,len,mult=2)', //ta.kcw(). Keltner Channels Width. The Keltner Channels Width is the difference between the upper and the lower Keltner Channels divided by the middle channel.
macd = 'macd(src,len)', //macd
mfi = 'mfi(src,len)', //Money Flow Index
nvi = 'nvi()', //Negative Volume Index
obv = 'obv()', //On Balance Volume
pvi = 'pvi()', //Positive Volume Index
pvt = 'pvt()', //Price Volume Trend
rise = 'rising(src,len)', //ta.rising() Test if the `source` series is now rising for `length` bars long. (Use its Input as another indicator output)
roc = 'roc(src,len)', //Rate of Change
rsi = 'rsi(src,len)', //Relative strength Index
smosc = 'smi_osc(src,len,fast=5, slow=34)', //smi Oscillator
smsig = 'smi_sig(src,len,fast=5, slow=34)', //smi Signal
stdev = 'stdev(src,len)', //Standart deviation
trix = 'trix(src,len)' , //the rate of change of a triple exponentially smoothed moving average.
tsi = 'tsi(src,len)', //True Strength Index
vari = 'variance(src,len)', //ta.variance(). Variance is the expectation of the squared deviation of a series from its mean (ta.sma), and it informally measures how far a set of numbers are spread out from their mean.
wilpc = 'willprc(src,len)', //Williams %R
wad = 'wad()', //Williams Accumulation/Distribution.
wvad = 'wvad()' //Williams Variable Accumulation/Distribution.
}
f_func(string, float, simple, float, float, float, simple) f_func Return selected indicator value with different parameters. New version. Use extra parameters for available indicators
Parameters:
string : FuncType_ indicator from the indicator list
float : src_ close, open, high, low,hl2, hlc3, ohlc4 or any
simple : int length_ indicator length
float : p1 extra parameter-1. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p2 extra parameter-2. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p3 extra parameter-3. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
simple : int version_ indicator version for backward compatibility. V1:dont use extra parameters p1,p2,p3 and use default values. V2: use extra parameters for available indicators
Returns: float Return calculated indicator value
fn_heikin(float, float, float, float) fn_heikin Return given src data (open, high,low,close) as heikin ashi candle values
Parameters:
float : o_ open value
float : h_ high value
float : l_ low value
float : c_ close value
Returns: float heikin ashi open, high,low,close vlues that will be used with plotcandle
fn_plotFunction(float, string, simple, bool) fn_plotFunction Return input src data with different plotting options
Parameters:
float : src_ indicator src_data or any other series.....
string : plotingType Ploting type of the function on the screen
simple : int stochlen_ length for plotingType for stochastic and PercentRank options
bool : plotSWMA Use SWMA for smoothing Ploting
Returns: float
fn_funcPlotV2(string, float, simple, float, float, float, simple, string, simple, bool, bool) fn_funcPlotV2 Return selected indicator value with different parameters. New version. Use extra parameters fora available indicators
Parameters:
string : FuncType_ indicator from the indicator list
float : src_data_ close, open, high, low,hl2, hlc3, ohlc4 or any
simple : int length_ indicator length
float : p1 extra parameter-1. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p2 extra parameter-2. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p3 extra parameter-3. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
simple : int version_ indicator version for backward compatibility. V1:dont use extra parameters p1,p2,p3 and use default values. V2: use extra parameters for available indicators
string : plotingType Ploting type of the function on the screen
simple : int stochlen_ length for plotingType for stochastic and PercentRank options
bool : plotSWMA Use SWMA for smoothing Ploting
bool : log_ Use log on function entries
Returns: float Return calculated indicator value
fn_factor(string, float, simple, float, float, float, simple, simple, string, simple, bool, bool) fn_factor Return selected indicator's factorization with given arguments
Parameters:
string : FuncType_ indicator from the indicator list
float : src_data_ close, open, high, low,hl2, hlc3, ohlc4 or any
simple : int length_ indicator length
float : p1 parameter-1. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p2 parameter-2. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p3 parameter-3. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
simple : int version_ indicator version for backward compatibility. V1:dont use extra parameters p1,p2,p3 and use default values. V2: use extra parameters for available indicators
simple : int fact_ Add double triple, Quatr factor to selected indicator (like converting EMA to 2-DEMA, 3-TEMA, 4-QEMA...)
string : plotingType Ploting type of the function on the screen
simple : int stochlen_ length for plotingType for stochastic and PercentRank options
bool : plotSWMA Use SWMA for smoothing Ploting
bool : log_ Use log on function entries
Returns: float Return result of the function
fn_plotCandles(string, simple, float, float, float, simple, string, simple, bool, bool, bool) fn_plotCandles Return selected indicator's candle values with different parameters also heikinashi is available
Parameters:
string : FuncType_ indicator from the indicator list
simple : int length_ indicator length
float : p1 parameter-1. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p2 parameter-2. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
float : p3 parameter-3. active on Version 2 for defining multi arguments indicator input value. ex: lagAdapt(src_, length_,LAPercLen_=p1,FPerc_=p2)
simple : int version_ indicator version for backward compatibility. V1:dont use extra parameters p1,p2,p3 and use default values. V2: use extra parameters for available indicators
string : plotingType Ploting type of the function on the screen
simple : int stochlen_ length for plotingType for stochastic and PercentRank options
bool : plotSWMA Use SWMA for smoothing Ploting
bool : log_ Use log on function entries
bool : plotheikin_ Use Heikin Ashi on Plot
Returns: float
[EG] MA ATR ChannelsGreetings - the aim of this indicator was to code a single indicator with a selectable moving average, so I could examine price relationships to MA's and Average True Range (ATR) bollinger type bands. You can obviously approach this tool in so many different ways so I am going to share first an overview of moving averages and a short overview of how I use this this indicator.
Simple ( SMA ) – A simple average of the past N (length) prices. Just add the price data for each N (bar) and divide the total by N.
Exponential ( EMA ) – An exponential moving average with a greater weight for recent prices. The weighting is exponential. An N-period EMA takes more than N data points into account and gradually dilutes past data’s effect.
Double Exponential ( DEMA ) - Same as an EMA , the Double exponential moving average , or DEMA , is a measure of a security's trending average price that gives the even more weight to recent price data. Aimed to help reduce lag.
Triple Exponential ( TEMA ) - Same as an EMA , the Triple exponential moving average , or TEMA , is a measure of a security's trending average price that gives the even more weight to recent price data than EMA or DEMA . Aimed to help reduce lag.
Weighted ( WMA ) – An average of the past N prices with a linear weighting, again giving greater weight to more recent prices.
Hull ( HMA ) - The Hull Moving Average (developed by Alan Hull) has the purpose of reducing lag, increasing responsiveness while at the same time eliminating noise. It emphasises recent prices over older ones, resulting in a fast-acting yet smooth moving average that can be used to identify the prevailing market trend.
Wilder's (RMA) - Wilder's smoothing is a type of exponential moving average . It takes one parameter, the period n, and price. Larger values for n will have a greater smoothing effect on the input data but will also create more lag. It is equivalent to a 2n-1 Exponential Moving Average . For example, a 10 period Wilder's smoothing is the same as a 19 period exponential moving average .
Symmetrically Weighted ( SWMA ) - Weight distribution starts from median of given period and it's reduced linearly to the sides so the ending and starting point of period have the least weight. It's smooth and fast but reacts late to trend changes on higher lengths (lookback).
Arnaud Legoux ( ALMA ) - Arnaud Legoux Moving Average removes small price fluctuations and enhances trend via applying a moving average twice, once from left to right, and once from right to left and combines both. At the end of this process the phase shift (price lag) commonly associated with moving averages is significantly reduced.
Volume-Weighted ( VWMA ) - A Volume-Weighted Moving Average gives a different weight to each closing price and this weight depends on the volume of that period. For example, the closing price of a day with high volume will have a greater weight on the moving average value.
Volume Weighted Average Price ( VWAP ) - Though not necessarily a MA - Volume-weighted average price ( VWAP ) is a ratio of the cumulative share price to the cumulative volume traded over a given time period and so I thought would be useful as an ATR tool. The VWAP is calculated using the opening price for each day and adjusting in real time right up until the close of the session. Thus, the calculation uses intraday data only.
So what is Average True Range ?
Average True Range is a measure of volatility . It's an area that represents roughly how much you can expect a security to change in price over a time period. Average true range is usually calculated by applying Wilders Smoothing to True Range. If you want regular ATR - use RMA as the input for the ATR. The ATR is then divided into periods based on derivatives of Phi (3.14) and Fibs (0.618, 1.618 etc.) You will notice price bounces off the lines. Look for patterns.
The indicator - consisting of 3 parts:
Price/Fast MA - this is an MA anywhere between 3-20 periods that is reflective of very recent price action. It is red when price is below - and green when above. Recommendations : SMA , EMA , WMA , HMA
Trend/Medium MA - this is a slower MA that you could set anywhere between 30 - 100 periods that is reflective of overall bull/bear market trend depending on both it's direction and whether the Price MA / price is lower or higher. Recommendations: EMA , WMA , VWMA , RMA, ALMA
Average True Range - this is a way to measure and visualise range the price may be capable of in - if it is towards or below the 2.1 multiplier - a bull reversal is more likely and vice versea. The multi's are set to factors of Pi and Fibonacci ratio's. Green channel means bullish, red channel means bearish. Gold means sign of a likely reversal. If the PMA enters the channel - it is likely the reversal is cancelled for a short period more.
Recommendations : RMA, EMA , VWMA , ALMA , SWMA , VWAP
How I use it :
First of all - Consider longs when channel is green - or going to bounce on a support line - and consider shorts based on the opposite. This is not a buy/sell indicator - this is a MAP to PRICE to give reference and meaning to price movements across multiple time frames - very useful when using with a volume indicator and an RSI. I personally use it on the 3m chart but change the TFM to 5 for 15m data.
If you wish to see any other more exotic or interesting MA's added please feel free to request them in the comments ! And thanks for checking out my first indicator
Multiple EMAAn exponential moving average (EMA) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average (SMA), which applies an equal weight to all observations in the period.
The EMA is a moving average that places a greater weight and significance on the most recent data points.
Like all moving averages, this technical indicator is used to produce buy and sell signals based on crossovers and divergences from the historical average.
Traders often use several different EMA lengths, such as 10-day, 50-day, and 200-day moving averages.
Points to remember:
Exponential moving averages are more sensitive to the recent price
EMA can signal good trades, but it can also keep you out of bad trades
EMA offers dynamic support and resistance levels, which is good for trailing Stop Loss
The EMA slope shape has hidden secrets
The rules for the EMA trading strategy can be modified to fit your own trading needs. We don’t claim this to be hard rules, but they are good on their own to make for a great trading strategy. Make sure you first test out the EMA strategy on a paper trading account before you risk any of your hard-earned money
Uptrick: Logarithmic Crypto Bands
Description :
Introduction
The `Uptrick: Logarithmic Crypto Bands` indicator introduces an innovative approach to technical analysis tailored specifically for the cryptocurrency markets. By leveraging logarithmic transformations combined with dynamic exponential bands, this indicator offers a sophisticated method for identifying critical support and resistance levels, assessing market trends, and evaluating volatility. Its unique approach stands out from traditional indicators by addressing the specific challenges of high volatility and erratic price movements inherent in cryptocurrency trading.
Originality and Usefulness
** 1. Unique Logarithmic Transformation: **
- Innovation : Unlike traditional indicators that often use raw price data, the Uptrick: Logarithmic Crypto Bands applies a logarithmic transformation to the closing prices: logPrice = math.log(close). This approach is original because it reduces the impact of extreme price fluctuations, providing a smoother and more stable price series. This transformation addresses a common issue in cryptocurrency markets where large price swings can obscure true market trends.
- Advantage : The logarithmic transformation compresses the price range, which allows traders to better identify long-term trends and reduce the noise caused by outlier price movements. This results in a more reliable basis for analysis and enhances the ability to detect meaningful market patterns.
**2. Dynamic Exponential Bands :**
- Innovation : The indicator employs exponential calculations to derive dynamic support and resistance levels based on a central base line : baseLine * math.pow(multiplier, n). Unlike static bands that remain fixed regardless of market conditions, these bands adjust dynamically according to market volatility.
- Advantage : The dynamic nature of the bands provides a more responsive and adaptive tool for traders. As market volatility changes, the bands widen or narrow accordingly, offering a more accurate reflection of potential support and resistance levels. This adaptability improves the tool's effectiveness in varying market conditions compared to static or traditional bands.
Detailed Description and Substantiation
**1. Logarithmic Price Calculation :**
- Code : ` logPrice = math.log(close)
- Description : This calculation converts the closing price into its logarithmic value. By compressing the price range, it minimizes the distortion caused by extreme price movements, which can be particularly pronounced in the volatile cryptocurrency markets.
- Purpose : To provide a stabilized price series that facilitates more accurate trend analysis and reduces the influence of erratic price fluctuations.
**2. Moving Averages of Logarithmic Prices :**
- ** Long-Term Moving Average :**
- Code : maLongLogPrice = ta.sma(logPrice, longLength)
longLength = 2000
- ** Description : A simple moving average of the logarithmic price over a long period. This average helps filter out short-term noise and provides insight into the long-term market trend.
- Purpose : To offer a perspective on the overall market direction, making it easier to identify enduring trends and distinguish them from short-term price movements.
- Short-Term Moving Average :
- Code : maShortLogPrice = ta.sma(logPrice, shortLength) shortLength = 900
- Description : A simple moving average of the logarithmic price over a shorter period. This component captures more immediate price trends and potential reversal points.
- Purpose : To detect short-term trends and changes in market direction, allowing traders to make timely trading decisions based on recent price action.
**3. Base Line Calculation :**
- Code : baseLine = math.exp(maShortLogPrice)
- Description : Converts the short-term moving average of the logarithmic price back to the original price scale. This base line serves as the central reference point for calculating the surrounding bands.
- Purpose : To establish a benchmark level from which the exponential bands are calculated, providing a central reference for assessing potential support and resistance levels.
**4. Band Calculation and Plotting :**
- ** Code :**
- Band 1: plot(baseLine * math.pow(multiplier, 1), color=color.new(color.yellow, 20), linewidth=1, title="Band 1")
- Band 2: plot(baseLine * math.pow(multiplier, 2), color=color.new(color.yellow, 20), linewidth=1, title="Band 2")
- Band 3: plot(baseLine * math.pow(multiplier, 3), color=color.new(color.yellow, 20), linewidth=1, title="Band 3")
- Band 4: plot(baseLine * math.pow(multiplier, 4), color=color.new(color.yellow, 20), linewidth=1, title="Band 4")
- Band 5: plot(baseLine * math.pow(multiplier, 5), color=color.new(color.yellow, 10), linewidth=1, title="Band 5")
- Band 6: plot(baseLine * math.pow(multiplier, 6), color=color.new(color.yellow, 0), linewidth=1, title="Band 6")
- * Multiplier : Set at 1.3, adjusts the spacing between bands to accommodate varying levels of market volatility.
- Description : Bands are plotted at exponential intervals from the base line. Each band represents a potential support or resistance level, with the spacing between them increasing exponentially. The color opacity of each band indicates its level of significance, with closer bands being more relevant for immediate trading decisions.
** How to Use the Indicator :**
**1. Identifying Support and Resistance Levels :**
- Support Levels : The lower bands, closer to the base line, can act as potential support levels. When the price approaches these bands from above, they may indicate areas where the price could stabilize or reverse direction.
- Resistance Levels : The upper bands, further from the base line, serve as resistance levels. When the price nears these bands from below, they can act as barriers to price movement, potentially leading to reversals or stalls.
**2. Confirming Trends :**
- Uptrend Confirmation : When the price consistently remains above the base line and moves towards higher bands, it signals a strong bullish trend. This confirmation helps traders capitalize on upward price movements.
- Downtrend Confirmation : When the price stays below the base line and approaches lower bands, it indicates a bearish trend. This confirmation assists traders in acting on downward price movements.
3. Analyzing Volatility :
- Wide Bands : Wider spacing between bands reflects higher market volatility. This indicates a more turbulent trading environment, where price movements are less predictable. Traders may need to adjust their strategies to handle increased volatility.
- Narrow Bands : Narrower bands suggest lower volatility and a more stable market environment. This can result in more predictable price movements and clearer trading signals.
**4. Entry and Exit Points :**
- Entry Points : Consider buying when the price bounces off the base line or a band, which could signal support in an uptrend.
- Exit Points : Evaluate selling or taking profits when the price nears upper bands or shows signs of reversal at these levels. This approach helps in locking in gains or minimizing losses during a downtrend.
**Chart Example:**
Here you can see how the price reacted getting closer to this level. All green circles show a bounce-off. So just from looking at the chart we can see a potential bounce again pretty soon.
** Disclosure :**
- ** Performance Claims :** The `Uptrick: Logarithmic Crypto Bands` indicator is designed to assist traders in analyzing price levels and trends. It is important to understand that this tool provides historical data analysis and does not guarantee future performance. The features and benefits described are based on historical market behavior and should not be seen as a prediction of future results. Traders should use this indicator as part of a broader trading strategy and consider other factors before making trading decisions.
[AIO] Multi Collection Moving Averages 140 MA TypesAll In One Multi Collection Moving Averages.
Since signing up 2 years ago, I have been collecting various Сollections.
I decided to get it into a decent shape and make it one of the biggest collections on TV, and maybe the entire internet.
And now I'm sharing my collection with you.
140 Different Types of Moving Averages are waiting for you.
Specifically :
"
AARMA | Adaptive Autonomous Recursive Moving Average
ADMA | Adjusted Moving Average
ADXMA | Average Directional Moving Average
ADXVMA | Average Directional Volatility Moving Average
AHMA | Ahrens Moving Average
ALF | Ehler Adaptive Laguerre Filter
ALMA | Arnaud Legoux Moving Average
ALSMA | Adaptive Least Squares
ALXMA | Alexander Moving Average
AMA | Adaptive Moving Average
ARI | Unknown
ARSI | Adaptive RSI Moving Average
AUF | Auto Filter
AUTL | Auto-Line
BAMA | Bryant Adaptive Moving Average
BFMA | Blackman Filter Moving Average
CMA | Corrected Moving Average
CORMA | Correlation Moving Average
COVEMA | Coefficient of Variation Weighted Exponential Moving Average
COVNA | Coefficient of Variation Weighted Moving Average
CTI | Coral Trend Indicator
DEC | Ehlers Simple Decycler
DEMA | Double EMA Moving Average
DEVS | Ehlers - Deviation Scaled Moving Average
DONEMA | Donchian Extremum Moving Average
DONMA | Donchian Moving Average
DSEMA | Double Smoothed Exponential Moving Average
DSWF | Damped Sine Wave Weighted Filter
DWMA | Double Weighted Moving Average
E2PBF | Ehlers 2-Pole Butterworth Filter
E2SSF | Ehlers 2-Pole Super Smoother Filter
E3PBF | Ehlers 3-Pole Butterworth Filter
E3SSF | Ehlers 3-Pole Super Smoother Filter
EDMA | Exponentially Deviating Moving Average (MZ EDMA)
EDSMA | Ehlers Dynamic Smoothed Moving Average
EEO | Ehlers Modified Elliptic Filter Optimum
EFRAMA | Ehlers Modified Fractal Adaptive Moving Average
EHMA | Exponential Hull Moving Average
EIT | Ehlers Instantaneous Trendline
ELF | Ehler Laguerre filter
EMA | Exponential Moving Average
EMARSI | EMARSI
EPF | Edge Preserving Filter
EPMA | End Point Moving Average
EREA | Ehlers Reverse Exponential Moving Average
ESSF | Ehlers Super Smoother Filter 2-pole
ETMA | Exponential Triangular Moving Average
EVMA | Elastic Volume Weighted Moving Average
FAMA | Following Adaptive Moving Average
FEMA | Fast Exponential Moving Average
FIBWMA | Fibonacci Weighted Moving Average
FLSMA | Fisher Least Squares Moving Average
FRAMA | Ehlers - Fractal Adaptive Moving Average
FX | Fibonacci X Level
GAUS | Ehlers - Gaussian Filter
GHL | Gann High Low
GMA | Gaussian Moving Average
GMMA | Geometric Mean Moving Average
HCF | Hybrid Convolution Filter
HEMA | Holt Exponential Moving Average
HKAMA | Hilbert based Kaufman Adaptive Moving Average
HMA | Harmonic Moving Average
HSMA | Hirashima Sugita Moving Average
HULL | Hull Moving Average
HULLT | Hull Triple Moving Average
HWMA | Henderson Weighted Moving Average
IE2 | Early T3 by Tim Tilson
IIRF | Infinite Impulse Response Filter
ILRS | Integral of Linear Regression Slope
JMA | Jurik Moving Average
KA | Unknown
KAMA | Kaufman Adaptive Moving Average & Apirine Adaptive MA
KIJUN | KIJUN
KIJUN2 | Kijun v2
LAG | Ehlers - Laguerre Filter
LCLSMA | 1LC-LSMA (1 line code lsma with 3 functions)
LEMA | Leader Exponential Moving Average
LLMA | Low-Lag Moving Average
LMA | Leo Moving Average
LP | Unknown
LRL | Linear Regression Line
LSMA | Least Squares Moving Average / Linear Regression Curve
LTB | Unknown
LWMA | Linear Weighted Moving Average
MAMA | MAMA - MESA Adaptive Moving Average
MAVW | Mavilim Weighted Moving Average
MCGD | McGinley Dynamic Moving Average
MF | Modular Filter
MID | Median Moving Average / Percentile Nearest Rank
MNMA | McNicholl Moving Average
MTMA | Unknown
MVSMA | Minimum Variance SMA
NLMA | Non-lag Moving Average
NWMA | Dürschner 3rd Generation Moving Average (New WMA)
PKF | Parametric Kalman Filter
PWMA | Parabolic Weighted Moving Average
QEMA | Quadruple Exponential Moving Average
QMA | Quick Moving Average
REMA | Regularized Exponential Moving Average
REPMA | Repulsion Moving Average
RGEMA | Range Exponential Moving Average
RMA | Welles Wilders Smoothing Moving Average
RMF | Recursive Median Filter
RMTA | Recursive Moving Trend Average
RSMA | Relative Strength Moving Average - based on RSI
RSRMA | Right Sided Ricker MA
RWMA | Regressively Weighted Moving Average
SAMA | Slope Adaptive Moving Average
SFMA | Smoother Filter Moving Average
SMA | Simple Moving Average
SSB | Senkou Span B
SSF | Ehlers - Super Smoother Filter P2
SSMA | Super Smooth Moving Average
STMA | Unknown
SWMA | Self-Weighted Moving Average
SW_MA | Sine-Weighted Moving Average
TEMA | Triple Exponential Moving Average
THMA | Triple Exponential Hull Moving Average
TL | Unknown
TMA | Triangular Moving Average
TPBF | Three-pole Ehlers Butterworth
TRAMA | Trend Regularity Adaptive Moving Average
TSF | True Strength Force
TT3 | Tilson (3rd Degree) Moving Average
VAMA | Volatility Adjusted Moving Average
VAMAF | Volume Adjusted Moving Average Function
VAR | Vector Autoregression Moving Average
VBMA | Variable Moving Average
VHMA | Vertical Horizontal Moving Average
VIDYA | Variable Index Dynamic Average
VMA | Volume Moving Average
VSO | Unknown
VWMA | Volume Weighted Moving Average
WCD | Unknown
WMA | Weighted Moving Average
XEMA | Optimized Exponential Moving Average
ZEMA | Zero Lag Moving Average
ZLDEMA | Zero-Lag Double Exponential Moving Average
ZLEMA | Ehlers - Zero Lag Exponential Moving Average
ZLTEMA | Zero-Lag Triple Exponential Moving Average
ZSMA | Zero-Lag Simple Moving Average
"
Don't forget that you can use any Moving Average not only for the chart but also for any of your indicators without affecting the code as in my example.
But remember that some MAs are not designed to work with anything other than a chart.
All MA and Code lists are sorted strictly alphabetically by short name (A-Z).
Each MA has its own number (ID) by which you can display the Moving Average you need.
Next to the ID selection there are tooltips with short names and their numbers. Use them.
The panel below will help you to read the Name of the selected MA.
Because of the size of the collection I think this is the optimal and most convenient use. Correct me if this is not the case.
Unknown - Some MAs I collected so long ago that I lost the full real name and couldn't find the authors. If you recognize them, please let me know.
I have deliberately simplified all MAs to input just Source and Length.
Because the collection is so large, it would be quite inconvenient and difficult to customize all MA functions (multipliers, offset, etc.).
If you need or like any MA you will still have to take it from my collection for your code.
I tried to leave the basic MA settings inside function in first strings.
I have tried to list most of the authors, but since the bulk of the collection was created a long time ago and was not intended for public publication I could not find all of them.
Some of the features were created from scratch or may have been slightly modified, so please be careful.
If you would like to improve this collection, please write to me in PM.
Also Credits, Likes, Awards, Loves and Thanks to :
@alexgrover
@allanster
@andre_007
@auroagwei
@blackcat1402
@bsharpe
@cheatcountry
@CrackingCryptocurrency
@Duyck
@ErwinBeckers
@everget
@glaz
@gotbeatz26107
@HPotter
@io72signals
@JacobAmos
@JoshuaMcGowan
@KivancOzbilgic
@LazyBear
@loxx
@LuxAlgo
@MightyZinger
@nemozny
@NGBaltic
@peacefulLizard50262
@RicardoSantos
@StalexBot
@ThiagoSchmitz
@TradingView
— 𝐀𝐧𝐝 𝐎𝐭𝐡𝐞𝐫𝐬 !
So just a Big Thank You to everyone who has ever and anywhere shared their codes.
Moving Average Compendium RefurbishedThis is my effort to bring together in a single script the widest range of moving averages possible.
I aggregated the calculation of averages within a library.
For more information about the library follow the link:
Basically this indicator is the visual result of this library.
You can choose the moving average and the script updates the chart as per the type.
The unique parameters of certain moving averages remain at their default values.
To have a rainbow of moving averages I also made an indicator:
Available moving averages:
AARMA = 'Adaptive Autonomous Recursive Moving Average'
ADEMA = '* Alpha-Decreasing Exponential Moving Average'
AHMA = 'Ahrens Moving Average'
ALMA = 'Arnaud Legoux Moving Average'
ALSMA = 'Adaptive Least Squares'
AUTOL = 'Auto-Line'
CMA = 'Corrective Moving average'
CORMA = 'Correlation Moving Average Price'
COVWEMA = 'Coefficient of Variation Weighted Exponential Moving Average'
COVWMA = 'Coefficient of Variation Weighted Moving Average'
DEMA = 'Double Exponential Moving Average'
DONCHIAN = 'Donchian Middle Channel'
EDMA = 'Exponentially Deviating Moving Average'
EDSMA = 'Ehlers Dynamic Smoothed Moving Average'
EFRAMA = '* Ehlrs Modified Fractal Adaptive Moving Average'
EHMA = 'Exponential Hull Moving Average'
EMA = 'Exponential Moving Average'
EPMA = 'End Point Moving Average'
ETMA = 'Exponential Triangular Moving Average'
EVWMA = 'Elastic Volume Weighted Moving Average'
FAMA = 'Following Adaptive Moving Average'
FIBOWMA = 'Fibonacci Weighted Moving Average'
FISHLSMA = 'Fisher Least Squares Moving Average'
FRAMA = 'Fractal Adaptive Moving Average'
GMA = 'Geometric Moving Average'
HKAMA = 'Hilbert based Kaufman\'s Adaptive Moving Average'
HMA = 'Hull Moving Average'
JURIK = 'Jurik Moving Average'
KAMA = 'Kaufman\'s Adaptive Moving Average'
LC_LSMA = '1LC-LSMA (1 line code lsma with 3 functions)'
LEOMA = 'Leo Moving Average'
LINWMA = 'Linear Weighted Moving Average'
LSMA = 'Least Squares Moving Average'
MAMA = 'MESA Adaptive Moving Average'
MCMA = 'McNicholl Moving Average'
MEDIAN = 'Median'
REGMA = 'Regularized Exponential Moving Average'
REMA = 'Range EMA'
REPMA = 'Repulsion Moving Average'
RMA = 'Relative Moving Average'
RSIMA = 'RSI Moving average'
RVWAP = '* Rolling VWAP'
SMA = 'Simple Moving Average'
SMMA = 'Smoothed Moving Average'
SRWMA = 'Square Root Weighted Moving Average'
SW_MA = 'Sine-Weighted Moving Average'
SWMA = '* Symmetrically Weighted Moving Average'
TEMA = 'Triple Exponential Moving Average'
THMA = 'Triple Hull Moving Average'
TREMA = 'Triangular Exponential Moving Average'
TRSMA = 'Triangular Simple Moving Average'
TT3 = 'Tillson T3'
VAMA = 'Volatility Adjusted Moving Average'
VIDYA = 'Variable Index Dynamic Average'
VWAP = '* VWAP'
VWMA = 'Volume-weighted Moving Average'
WMA = 'Weighted Moving Average'
WWMA = 'Welles Wilder Moving Average'
XEMA = 'Optimized Exponential Moving Average'
ZEMA = 'Zero-Lag Exponential Moving Average'
ZSMA = 'Zero-Lag Simple Moving Average'
Moving Averages RefurbishedIntroduction
This is a collection of multiple moving averages, where you can have a rainbow of moving averages with different types that can be defined by the user.
There are already other indicators in this rainbow style, however certain averages are absent in certain indicators and present in others,
needing the merge to have a more complete solution.
Resources
Here there is the possibility to individually define each moving average.
In addition, it is possible to adjust some details, such as themes, coloring and periods.
Regarding the calculation of averages, credit goes to the following authors.
What I've done here is to group these averages together and allow them to combine.
Credits
TradingView
PineCoders
CrackingCryptocurrency
MightyZinger
Alex Orekhov (everget)
alexgrover
paragjyoti2012
Moving averages available
1. Exponential Moving Average
2. Simple Moving Average
3. Relative Moving Average
4. Weighted Moving Average
5. Ehlers Dynamic Smoothed Moving Average
6. Double Exponential Moving Average
7. Triple Exponential Moving Average
8. Smoothed Moving Average
9. Hull Moving Average
10. Fractal Adaptive Moving Average
11. Kaufman's Adaptive Moving Average
12. Volatility Adjusted Moving Average
13. Jurik Moving Average
14. Optimized Exponential Moving Average
15. Exponential Hull Moving Average
16. Arnaud Legoux Moving Average
17. Coefficient of Variation Weighted Exponential Moving Average
18. Coefficient of Variation Weighted Moving Average
19. * Ehlrs Modified Fractal Adaptive Moving Average
20. Exponential Triangular Moving Average
21. Least Squares Moving Average
22. RSI Moving average
23. Simple Triangular Moving Average
24. Triple Hull Moving Average
25. Variable Index Dynamic Average
26. Volume-weighted Moving Average
27. Zero-Lag Exponential Moving Average
28. Zero-Lag Simple Moving Average
29. Elastic Volume Weighted Moving Average
30. Tillson T3
31. Geometric Moving Average
32. Welles Wilder Moving Average
33. Adjusted Moving Average
34. Corrective Moving average
35. Exponentially Deviating Moving Average
36. EMA Range
37. Sine-Weighted Moving Average
38. Adaptive Moving Average TABLE
39. Following Adaptive Moving Average
40. Hilbert based Kaufman's Adaptive Moving Average
41. Median
42. * VWAP
43. * Rolling VWAP
44. Triangular Simple Moving Average
45. Triangular Exponential Moving Average
46. Moving Average Price Correlation
47. Regularized Exponential Moving Average
48. Repulsion Moving Average
49. * Symmetrically Weighted Moving Average
* fixed period averages
BAERMThe Bitcoin Auto-correlation Exchange Rate Model: A Novel Two Step Approach
THIS IS NOT FINANCIAL ADVICE. THIS ARTICLE IS FOR EDUCATIONAL AND ENTERTAINMENT PURPOSES ONLY.
If you enjoy this software and information, please consider contributing to my lightning address
Prelude
It has been previously established that the Bitcoin daily USD exchange rate series is extremely auto-correlated
In this article, we will utilise this fact to build a model for Bitcoin/USD exchange rate. But not a model for predicting the exchange rate, but rather a model to understand the fundamental reasons for the Bitcoin to have this exchange rate to begin with.
This is a model of sound money, scarcity and subjective value.
Introduction
Bitcoin, a decentralised peer to peer digital value exchange network, has experienced significant exchange rate fluctuations since its inception in 2009. In this article, we explore a two-step model that reasonably accurately captures both the fundamental drivers of Bitcoin’s value and the cyclical patterns of bull and bear markets. This model, whilst it can produce forecasts, is meant more of a way of understanding past exchange rate changes and understanding the fundamental values driving the ever increasing exchange rate. The forecasts from the model are to be considered inconclusive and speculative only.
Data preparation
To develop the BAERM, we used historical Bitcoin data from Coin Metrics, a leading provider of Bitcoin market data. The dataset includes daily USD exchange rates, block counts, and other relevant information. We pre-processed the data by performing the following steps:
Fixing date formats and setting the dataset’s time index
Generating cumulative sums for blocks and halving periods
Calculating daily rewards and total supply
Computing the log-transformed price
Step 1: Building the Base Model
To build the base model, we analysed data from the first two epochs (time periods between Bitcoin mining reward halvings) and regressed the logarithm of Bitcoin’s exchange rate on the mining reward and epoch. This base model captures the fundamental relationship between Bitcoin’s exchange rate, mining reward, and halving epoch.
where Yt represents the exchange rate at day t, Epochk is the kth epoch (for that t), and epsilont is the error term. The coefficients beta0, beta1, and beta2 are estimated using ordinary least squares regression.
Base Model Regression
We use ordinary least squares regression to estimate the coefficients for the betas in figure 2. In order to reduce the possibility of over-fitting and ensure there is sufficient out of sample for testing accuracy, the base model is only trained on the first two epochs. You will notice in the code we calculate the beta2 variable prior and call it “phaseplus”.
The code below shows the regression for the base model coefficients:
\# Run the regression
mask = df\ < 2 # we only want to use Epoch's 0 and 1 to estimate the coefficients for the base model
reg\_X = df.loc\ [mask, \ \].shift(1).iloc\
reg\_y = df.loc\ .iloc\
reg\_X = sm.add\_constant(reg\_X)
ols = sm.OLS(reg\_y, reg\_X).fit()
coefs = ols.params.values
print(coefs)
The result of this regression gives us the coefficients for the betas of the base model:
\
or in more human readable form: 0.029, 0.996869586, -0.00043. NB that for the auto-correlation/momentum beta, we did NOT round the significant figures at all. Since the momentum is so important in this model, we must use all available significant figures.
Fundamental Insights from the Base Model
Momentum effect: The term 0.997 Y suggests that the exchange rate of Bitcoin on a given day (Yi) is heavily influenced by the exchange rate on the previous day. This indicates a momentum effect, where the price of Bitcoin tends to follow its recent trend.
Momentum effect is a phenomenon observed in various financial markets, including stocks and other commodities. It implies that an asset’s price is more likely to continue moving in its current direction, either upwards or downwards, over the short term.
The momentum effect can be driven by several factors:
Behavioural biases: Investors may exhibit herding behaviour or be subject to cognitive biases such as confirmation bias, which could lead them to buy or sell assets based on recent trends, reinforcing the momentum.
Positive feedback loops: As more investors notice a trend and act on it, the trend may gain even more traction, leading to a self-reinforcing positive feedback loop. This can cause prices to continue moving in the same direction, further amplifying the momentum effect.
Technical analysis: Many traders use technical analysis to make investment decisions, which often involves studying historical exchange rate trends and chart patterns to predict future exchange rate movements. When a large number of traders follow similar strategies, their collective actions can create and reinforce exchange rate momentum.
Impact of halving events: In the Bitcoin network, new bitcoins are created as a reward to miners for validating transactions and adding new blocks to the blockchain. This reward is called the block reward, and it is halved approximately every four years, or every 210,000 blocks. This event is known as a halving.
The primary purpose of halving events is to control the supply of new bitcoins entering the market, ultimately leading to a capped supply of 21 million bitcoins. As the block reward decreases, the rate at which new bitcoins are created slows down, and this can have significant implications for the price of Bitcoin.
The term -0.0004*(50/(2^epochk) — (epochk+1)²) accounts for the impact of the halving events on the Bitcoin exchange rate. The model seems to suggest that the exchange rate of Bitcoin is influenced by a function of the number of halving events that have occurred.
Exponential decay and the decreasing impact of the halvings: The first part of this term, 50/(2^epochk), indicates that the impact of each subsequent halving event decays exponentially, implying that the influence of halving events on the Bitcoin exchange rate diminishes over time. This might be due to the decreasing marginal effect of each halving event on the overall Bitcoin supply as the block reward gets smaller and smaller.
This is antithetical to the wrong and popular stock to flow model, which suggests the opposite. Given the accuracy of the BAERM, this is yet another reason to question the S2F model, from a fundamental perspective.
The second part of the term, (epochk+1)², introduces a non-linear relationship between the halving events and the exchange rate. This non-linear aspect could reflect that the impact of halving events is not constant over time and may be influenced by various factors such as market dynamics, speculation, and changing market conditions.
The combination of these two terms is expressed by the graph of the model line (see figure 3), where it can be seen the step from each halving is decaying, and the step up from each halving event is given by a parabolic curve.
NB - The base model has been trained on the first two halving epochs and then seeded (i.e. the first lag point) with the oldest data available.
Constant term: The constant term 0.03 in the equation represents an inherent baseline level of growth in the Bitcoin exchange rate.
In any linear or linear-like model, the constant term, also known as the intercept or bias, represents the value of the dependent variable (in this case, the log-scaled Bitcoin USD exchange rate) when all the independent variables are set to zero.
The constant term indicates that even without considering the effects of the previous day’s exchange rate or halving events, there is a baseline growth in the exchange rate of Bitcoin. This baseline growth could be due to factors such as the network’s overall growth or increasing adoption, or changes in the market structure (more exchanges, changes to the regulatory environment, improved liquidity, more fiat on-ramps etc).
Base Model Regression Diagnostics
Below is a summary of the model generated by the OLS function
OLS Regression Results
\==============================================================================
Dep. Variable: logprice R-squared: 0.999
Model: OLS Adj. R-squared: 0.999
Method: Least Squares F-statistic: 2.041e+06
Date: Fri, 28 Apr 2023 Prob (F-statistic): 0.00
Time: 11:06:58 Log-Likelihood: 3001.6
No. Observations: 2182 AIC: -5997.
Df Residuals: 2179 BIC: -5980.
Df Model: 2
Covariance Type: nonrobust
\==============================================================================
coef std err t P>|t| \
\------------------------------------------------------------------------------
const 0.0292 0.009 3.081 0.002 0.011 0.048
logprice 0.9969 0.001 1012.724 0.000 0.995 0.999
phaseplus -0.0004 0.000 -2.239 0.025 -0.001 -5.3e-05
\==============================================================================
Omnibus: 674.771 Durbin-Watson: 1.901
Prob(Omnibus): 0.000 Jarque-Bera (JB): 24937.353
Skew: -0.765 Prob(JB): 0.00
Kurtosis: 19.491 Cond. No. 255.
\==============================================================================
Below we see some regression diagnostics along with the regression itself.
Diagnostics: We can see that the residuals are looking a little skewed and there is some heteroskedasticity within the residuals. The coefficient of determination, or r2 is very high, but that is to be expected given the momentum term. A better r2 is manually calculated by the sum square of the difference of the model to the untrained data. This can be achieved by the following code:
\# Calculate the out-of-sample R-squared
oos\_mask = df\ >= 2
oos\_actual = df.loc\
oos\_predicted = df.loc\
residuals\_oos = oos\_actual - oos\_predicted
SSR = np.sum(residuals\_oos \*\* 2)
SST = np.sum((oos\_actual - oos\_actual.mean()) \*\* 2)
R2\_oos = 1 - SSR/SST
print("Out-of-sample R-squared:", R2\_oos)
The result is: 0.84, which indicates a very close fit to the out of sample data for the base model, which goes some way to proving our fundamental assumption around subjective value and sound money to be accurate.
Step 2: Adding the Damping Function
Next, we incorporated a damping function to capture the cyclical nature of bull and bear markets. The optimal parameters for the damping function were determined by regressing on the residuals from the base model. The damping function enhances the model’s ability to identify and predict bull and bear cycles in the Bitcoin market. The addition of the damping function to the base model is expressed as the full model equation.
This brings me to the question — why? Why add the damping function to the base model, which is arguably already performing extremely well out of sample and providing valuable insights into the exchange rate movements of Bitcoin.
Fundamental reasoning behind the addition of a damping function:
Subjective Theory of Value: The cyclical component of the damping function, represented by the cosine function, can be thought of as capturing the periodic fluctuations in market sentiment. These fluctuations may arise from various factors, such as changes in investor risk appetite, macroeconomic conditions, or technological advancements. Mathematically, the cyclical component represents the frequency of these fluctuations, while the phase shift (α and β) allows for adjustments in the alignment of these cycles with historical data. This flexibility enables the damping function to account for the heterogeneity in market participants’ preferences and expectations, which is a key aspect of the subjective theory of value.
Time Preference and Market Cycles: The exponential decay component of the damping function, represented by the term e^(-0.0004t), can be linked to the concept of time preference and its impact on market dynamics. In financial markets, the discounting of future cash flows is a common practice, reflecting the time value of money and the inherent uncertainty of future events. The exponential decay in the damping function serves a similar purpose, diminishing the influence of past market cycles as time progresses. This decay term introduces a time-dependent weight to the cyclical component, capturing the dynamic nature of the Bitcoin market and the changing relevance of past events.
Interactions between Cyclical and Exponential Decay Components: The interplay between the cyclical and exponential decay components in the damping function captures the complex dynamics of the Bitcoin market. The damping function effectively models the attenuation of past cycles while also accounting for their periodic nature. This allows the model to adapt to changing market conditions and to provide accurate predictions even in the face of significant volatility or structural shifts.
Now we have the fundamental reasoning for the addition of the function, we can explore the actual implementation and look to other analogies for guidance —
Financial and physical analogies to the damping function:
Mathematical Aspects: The exponential decay component, e^(-0.0004t), attenuates the amplitude of the cyclical component over time. This attenuation factor is crucial in modelling the diminishing influence of past market cycles. The cyclical component, represented by the cosine function, accounts for the periodic nature of market cycles, with α determining the frequency of these cycles and β representing the phase shift. The constant term (+3) ensures that the function remains positive, which is important for practical applications, as the damping function is added to the rest of the model to obtain the final predictions.
Analogies to Existing Damping Functions: The damping function in the BAERM is similar to damped harmonic oscillators found in physics. In a damped harmonic oscillator, an object in motion experiences a restoring force proportional to its displacement from equilibrium and a damping force proportional to its velocity. The equation of motion for a damped harmonic oscillator is:
x’’(t) + 2γx’(t) + ω₀²x(t) = 0
where x(t) is the displacement, ω₀ is the natural frequency, and γ is the damping coefficient. The damping function in the BAERM shares similarities with the solution to this equation, which is typically a product of an exponential decay term and a sinusoidal term. The exponential decay term in the BAERM captures the attenuation of past market cycles, while the cosine term represents the periodic nature of these cycles.
Comparisons with Financial Models: In finance, damped oscillatory models have been applied to model interest rates, stock prices, and exchange rates. The famous Black-Scholes option pricing model, for instance, assumes that stock prices follow a geometric Brownian motion, which can exhibit oscillatory behavior under certain conditions. In fixed income markets, the Cox-Ingersoll-Ross (CIR) model for interest rates also incorporates mean reversion and stochastic volatility, leading to damped oscillatory dynamics.
By drawing on these analogies, we can better understand the technical aspects of the damping function in the BAERM and appreciate its effectiveness in modelling the complex dynamics of the Bitcoin market. The damping function captures both the periodic nature of market cycles and the attenuation of past events’ influence.
Conclusion
In this article, we explored the Bitcoin Auto-correlation Exchange Rate Model (BAERM), a novel 2-step linear regression model for understanding the Bitcoin USD exchange rate. We discussed the model’s components, their interpretations, and the fundamental insights they provide about Bitcoin exchange rate dynamics.
The BAERM’s ability to capture the fundamental properties of Bitcoin is particularly interesting. The framework underlying the model emphasises the importance of individuals’ subjective valuations and preferences in determining prices. The momentum term, which accounts for auto-correlation, is a testament to this idea, as it shows that historical price trends influence market participants’ expectations and valuations. This observation is consistent with the notion that the price of Bitcoin is determined by individuals’ preferences based on past information.
Furthermore, the BAERM incorporates the impact of Bitcoin’s supply dynamics on its price through the halving epoch terms. By acknowledging the significance of supply-side factors, the model reflects the principles of sound money. A limited supply of money, such as that of Bitcoin, maintains its value and purchasing power over time. The halving events, which reduce the block reward, play a crucial role in making Bitcoin increasingly scarce, thus reinforcing its attractiveness as a store of value and a medium of exchange.
The constant term in the model serves as the baseline for the model’s predictions and can be interpreted as an inherent value attributed to Bitcoin. This value emphasizes the significance of the underlying technology, network effects, and Bitcoin’s role as a medium of exchange, store of value, and unit of account. These aspects are all essential for a sound form of money, and the model’s ability to account for them further showcases its strength in capturing the fundamental properties of Bitcoin.
The BAERM offers a potential robust and well-founded methodology for understanding the Bitcoin USD exchange rate, taking into account the key factors that drive it from both supply and demand perspectives.
In conclusion, the Bitcoin Auto-correlation Exchange Rate Model provides a comprehensive fundamentally grounded and hopefully useful framework for understanding the Bitcoin USD exchange rate.
Machine Learning: SuperTrend Strategy TP/SL [YinYangAlgorithms]The SuperTrend is a very useful Indicator to display when trends have shifted based on the Average True Range (ATR). Its underlying ideology is to calculate the ATR using a fixed length and then multiply it by a factor to calculate the SuperTrend +/-. When the close crosses the SuperTrend it changes direction.
This Strategy features the Traditional SuperTrend Calculations with Machine Learning (ML) and Take Profit / Stop Loss applied to it. Using ML on the SuperTrend allows for the ability to sort data from previous SuperTrend calculations. We can filter the data so only previous SuperTrends that follow the same direction and are within the distance bounds of our k-Nearest Neighbour (KNN) will be added and then averaged. This average can either be achieved using a Mean or with an Exponential calculation which puts added weight on the initial source. Take Profits and Stop Losses are then added to the ML SuperTrend so it may capitalize on Momentum changes meanwhile remaining in the Trend during consolidation.
By applying Machine Learning logic and adding a Take Profit and Stop Loss to the Traditional SuperTrend, we may enhance its underlying calculations with potential to withhold the trend better. The main purpose of this Strategy is to minimize losses and false trend changes while maximizing gains. This may be achieved by quick reversals of trends where strategic small losses are taken before a large trend occurs with hopes of potentially occurring large gain. Due to this logic, the Win/Loss ratio of this Strategy may be quite poor as it may take many small marginal losses where there is consolidation. However, it may also take large gains and capitalize on strong momentum movements.
Tutorial:
In this example above, we can get an idea of what the default settings may achieve when there is momentum. It focuses on attempting to hit the Trailing Take Profit which moves in accord with the SuperTrend just with a multiplier added. When momentum occurs it helps push the SuperTrend within it, which on its own may act as a smaller Trailing Take Profit of its own accord.
We’ve highlighted some key points from the last example to better emphasize how it works. As you can see, the White Circle is where profit was taken from the ML SuperTrend simply from it attempting to switch to a Bullish (Buy) Trend. However, that was rejected almost immediately and we went back to our Bearish (Sell) Trend that ended up resulting in our Take Profit being hit (Yellow Circle). This Strategy aims to not only capitalize on the small profits from SuperTrend to SuperTrend but to also capitalize when the Momentum is so strong that the price moves X% away from the SuperTrend and is able to hit the Take Profit location. This Take Profit addition to this Strategy is crucial as momentum may change state shortly after such drastic price movements; and if we were to simply wait for it to come back to the SuperTrend, we may lose out on lots of potential profit.
If you refer to the Yellow Circle in this example, you’ll notice what was talked about in the Summary/Overview above. During periods of consolidation when there is little momentum and price movement and we don’t have any Stop Loss activated, you may see ‘Signal Flashing’. Signal Flashing is when there are Buy and Sell signals that keep switching back and forth. During this time you may be taking small losses. This is a normal part of this Strategy. When a signal has finally been confirmed by Momentum, is when this Strategy shines and may produce the profit you desire.
You may be wondering, what causes these jagged like patterns in the SuperTrend? It's due to the ML logic, and it may be a little confusing, but essentially what is happening is the Fast Moving SuperTrend and the Slow Moving SuperTrend are creating KNN Min and Max distances that are extreme due to (usually) parabolic movement. This causes fewer values to be added to and averaged within the ML and causes less smooth and more exponential drastic movements. This is completely normal, and one of the perks of using k-Nearest Neighbor for ML calculations. If you don’t know, the Min and Max Distance allowed is derived from the most recent(0 index of data array) to KNN Length. So only SuperTrend values that exhibit distances within these Min/Max will be allowed into the average.
Since the KNN ML logic can cause these exponential movements in the SuperTrend, they likewise affect its Take Profit. The Take Profit may benefit from this movement like displayed in the example above which helped it claim profit before then exhibiting upwards movement.
By default our Stop Loss Multiplier is kept quite low at 0.0000025. Keeping it low may help to reduce some Signal Flashing while not taking extra losses more so than not using it at all. However, if we increase it even more to say 0.005 like is shown in the example above. It can really help the trend keep momentum. Please note, although previous results don’t imply future results, at 0.0000025 Stop Loss we are currently exhibiting 69.27% profit while at 0.005 Stop Loss we are exhibiting 33.54% profit. This just goes to show that although there may be less Signal Flashing, it may not result in more profit.
We will conclude our Tutorial here. Hopefully this has given you some insight as to how Machine Learning, combined with Trailing Take Profit and Stop Loss may have positive effects on the SuperTrend when turned into a Strategy.
Settings:
SuperTrend:
ATR Length: ATR Length used to create the Original Supertrend.
Factor: Multiplier used to create the Original Supertrend.
Stop Loss Multiplier: 0 = Don't use Stop Loss. Stop loss can be useful for helping to prevent false signals but also may result in more loss when hit and less profit when switching trends.
Take Profit Multiplier: Take Profits can be useful within the Supertrend Strategy to stop the price reverting all the way to the Stop Loss once it's been profitable.
Machine Learning:
Only Factor Same Trend Direction: Very useful for ensuring that data used in KNN is not manipulated by different SuperTrend Directional data. Please note, it doesn't affect KNN Exponential.
Rationalized Source Type: Should we Rationalize only a specific source, All or None?
Machine Learning Type: Are we using a Simple ML Average, KNN Mean Average, KNN Exponential Average or None?
Machine Learning Smoothing Type: How should we smooth our Fast and Slow ML Datas to be used in our KNN Distance calculation? SMA, EMA or VWMA?
KNN Distance Type: We need to check if distance is within the KNN Min/Max distance, which distance checks are we using.
Machine Learning Length: How far back is our Machine Learning going to keep data for.
k-Nearest Neighbour (KNN) Length: How many k-Nearest Neighbours will we account for?
Fast ML Data Length: What is our Fast ML Length?? This is used with our Slow Length to create our KNN Distance.
Slow ML Data Length: What is our Slow ML Length?? This is used with our Fast Length to create our KNN Distance.
If you have any questions, comments, ideas or concerns please don't hesitate to contact us.
HAPPY TRADING!
Catching the Bottom (by Coinrule)This script utilises the RSI and EMA indicators to enter and close the trade.
The relative strength index (RSI) is a momentum indicator used in technical analysis. RSI measures the speed and magnitude of a security's recent price changes to evaluate overvalued or undervalued conditions in the price of that security. The RSI is displayed as an oscillator (a line graph) on a scale of zero to 100. The RSI can do more than point to overbought and oversold securities. It can also indicate securities that may be primed for a trend reversal or corrective pullback in price. It can signal when to buy and sell. Traditionally, an RSI reading of 70 or above indicates an overbought situation. A reading of 30 or below indicates an oversold condition.
An exponential moving average (EMA) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average simple moving average (SMA), which applies an equal weight to all observations in the period.
The strategy enters and exits the trade based on the following conditions.
ENTRY
RSI has a decrease of 3.
RSI <40.
EMA100 has crossed above the EMA50.
EXIT
RSI is greater than 65.
EMA9 has crossed above EMA50.
This strategy is back tested from 1 April 2022 to simulate how the strategy would work in a bear market and provides good returns.
Pairs that produce very strong results include ETH on the 5m timeframe, BNB on 5m timeframe, XRP on the 45m timeframe, MATIC on the 30m timeframe and MATIC on the 2H timeframe.
The strategy assumes each order is using 30% of the available coins to make the results more realistic and to simulate you only ran this strategy on 30% of your holdings. A trading fee of 0.1% is also taken into account and is aligned to the base fee applied on Binance.
EMA curvesPlot EMAs for lengths 9, 21, 55 ,100, 200
An exponential moving average (EMA) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average simple moving average (SMA), which applies an equal weight to all observations in the period.
Fukuiz Octa-EMA + Ichimoku (Strategy)This strategy is based EMA of 8 different period and Ichimoku Cloud which works better in 1hr 4hr and daily time frame.
#A brief introduction to Ichimoku #
The Ichimoku Cloud is a collection of technical indicators that show support and resistance levels, as well as momentum and trend direction. It does this by taking multiple averages and plotting them on a chart. It also uses these figures to compute a “cloud” that attempts to forecast where the price may find support or resistance in the future.
#A brief introduction to EMA#
An exponential moving average ( EMA ) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average . An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average ( SMA ), which applies an equal weight to all observations in the period.
#How to use#
The strategy will give entry points itself, you can monitor and take profit manually(recommended), or you can use the exit setup.
EMA (Color) = Bullish trend
EMA (Gray) = Bearish trend
#Condition#
Buy = All Ema (color) above the cloud.
SELL= All Ema turn to gray color.
Fukuiz Octa-EMA + IchimokuThis indicator base on EMA of 8 different period and Ichimoku Cloud.
#A brief introduction to Ichimoku #
The Ichimoku Cloud is a collection of technical indicators that show support and resistance levels, as well as momentum and trend direction. It does this by taking multiple averages and plotting them on a chart. It also uses these figures to compute a “cloud” that attempts to forecast where the price may find support or resistance in the future.
#A brief introduction to EMA#
An exponential moving average (EMA) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average (SMA), which applies an equal weight to all observations in the period.
I combine this together to help you reduce the false signals in Ichimoku.
#How to use#
EMA (Color) = Bullish trend
EMA (Gray) = Bearish trend
#Buy condition#
Buy = All Ema(color) above the cloud.
#Sell condition#
SELL= All Ema turn to gray color.
Two EMA Cross+ IndicatorHello traders!
Today we gonna demonstrate out heuristic of classical EMA Indicator. We decided to simplify your trading staff and add some meta data. So, let’s look at it from the very beginning and initially speak about what EMA is and then I’ll tell you why our indicator is extremely convenient and useful.
So, what is EMA? An exponential moving average ( EMA ) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average . An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average ( SMA ), which applies an equal weight to all observations in the period.
Key takeaways:
-The EMA is a moving average that places a greater weight and significance on the most recent data points.
-Like all moving averages, this technical indicator is used to produce buy and sell signals based on crossovers and divergences from the historical average.
As you know, EMA Cross is one of basic and most popular Entry Indicators. It’s kinda easy to understand and even easier to use. This indicator consists of two EMAs - fast (red line) and slow (blue line). Fast EMA is EMA of less length that the fast EMA (default parameter is 9). Thus, it reacts the price change more actively than the slow. We can say that it takes into consideration the most actual price movements. Speaking about slow EMA (default parameter is 30) it’s more inert and it’s more difficult to change its action vastly. We can say that the EMA «looks» at the historical data more accurate, but doesn’t forget about actual price movements.
But how it works? Trivial. When the fast EMA crosses the slow bellow, it provides bearish signal, whereas when it crosses it above, it’s bullish signal. Even more, we added some «confirmation» factor. As you know, when the price is above the slow EMA, the slow EMA plays the role of support line for price and means that the price is in uptrend. Thus, when we see the cross above and it takes place under the price, we called it «strong Bullish Signal». When the price is bellow the slow EMA, slow EMA is resistance. Thus, when we see the cross bellow and it’s under the slow EMA, we called it «strong Bearish Signal».
To make your trading process easier, we plotted the places of crosses on the chart and added the descriptions of the crosses. The flags mean the place of cross. The default parameters have nice backtest on 1H chart. However, you can also change them depending on your goals and the time period. The places of cross looks like flags (red flag is «bearish» cross, green - «bullish»). As you can see, it’s really convenient.
I hope you’ll enjoy our heuristic of classical EMA Cross. We are sure that the meta data that we are taking into consideration makes the signals more accurate and the deals more profitable. The SkyRock Team with support of Trading View try to make your trading process more successful and profitable. Every day we works in conjunction to boost both your skills and trading balance. We hope, it’s really useful for you, dear traders!
MyLibraryLibrary "MyLibrary"
This library contains various trading strategies and utility functions for Pine Script.
simple_moving_average(src, length)
simple_moving_average
@description Calculates the Simple Moving Average (SMA) of a given series.
Parameters:
src (float) : (series float) The input series (e.g., close prices).
length (int) : (int) The number of periods to use for the SMA calculation.
Returns: (series float) The calculated SMA series.
exponential_moving_average(src, length)
exponential_moving_average
@description Calculates the Exponential Moving Average (EMA) of a given series.
Parameters:
src (float) : (series float) The input series (e.g., close prices).
length (simple int) : (int) The number of periods to use for the EMA calculation.
Returns: (series float) The calculated EMA series.
safe_division(numerator, denominator)
safe_division
@description Performs division with error handling for division by zero.
Parameters:
numerator (float) : (float) The numerator for the division.
denominator (float) : (float) The denominator for the division.
Returns: (float) The result of the division, or na if the denominator is zero.
strategy_moving_average_crossover(shortLength, longLength)
strategy_moving_average_crossover
@description Implements a Moving Average Crossover strategy.
Parameters:
shortLength (int) : (int) The length for the short period SMA.
longLength (int) : (int) The length for the long period SMA.
Returns: (series float, series float, series bool, series bool) The short SMA, long SMA, crossover signals, and crossunder signals.
strategy_rsi(rsiLength, overbought, oversold)
strategy_rsi
@description Implements an RSI-based trading strategy.
Parameters:
rsiLength (simple int) : (int) The length for the RSI calculation.
overbought (float) : (float) The overbought threshold.
oversold (float) : (float) The oversold threshold.
Returns: (series float, series bool, series bool) The RSI values, long signals, and short signals.
ichimoku_cloud(convPeriod, basePeriod, spanBPeriod, laggingSpanPeriod)
ichimoku_cloud
@description Computes Ichimoku Cloud components.
Parameters:
convPeriod (int) : (int) The conversion line period.
basePeriod (int) : (int) The base line period.
spanBPeriod (int)
laggingSpanPeriod (int)
Returns: (series float, series float, series float, series float, series float) The conversion line, base line, leading span A, leading span B, and lagging span.
strategy_ichimoku_conversion_baseline()
strategy_ichimoku_conversion_baseline
@description Implements an Ichimoku Conversion Line and Baseline strategy.
Returns: (series float, series float, series bool, series bool) The conversion line, baseline, crossover signals, and crossunder signals.
debug_print(labelText, value, barIndex)
debug_print
@description Prints values to the chart for debugging purposes.
Parameters:
labelText (string) : (string) The label text.
value (float) : (float) The value to display.
barIndex (int) : (int) The bar index where the label should be displayed.
Chande Kroll Trend Strategy (SPX, 1H) | PINEINDICATORSThe "Chande Kroll Stop Strategy" is designed to optimize trading on the SPX using a 1-hour timeframe. This strategy effectively combines the Chande Kroll Stop indicator with a Simple Moving Average (SMA) to create a robust method for identifying long entry and exit points. This detailed description will explain the components, rationale, and usage to ensure compliance with TradingView's guidelines and help traders understand the strategy's utility and application.
Objective
The primary goal of this strategy is to identify potential long trading opportunities in the SPX by leveraging volatility-adjusted stop levels and trend-following principles. It aims to capture upward price movements while managing risk through dynamically calculated stops.
Chande Kroll Stop Parameters:
Calculation Mode: Offers "Linear" and "Exponential" options for position size calculation. The default mode is "Exponential."
Risk Multiplier: An adjustable multiplier for risk management and position sizing, defaulting to 5.
ATR Period: Defines the period for calculating the Average True Range (ATR), with a default of 10.
ATR Multiplier: A multiplier applied to the ATR to set stop levels, defaulting to 3.
Stop Length: Period used to determine the highest high and lowest low for stop calculation, defaulting to 21.
SMA Length: Period for the Simple Moving Average, defaulting to 21.
Calculation Details:
ATR Calculation: ATR is calculated over the specified period to measure market volatility.
Chande Kroll Stop Calculation:
High Stop: The highest high over the stop length minus the ATR multiplied by the ATR multiplier.
Low Stop: The lowest low over the stop length plus the ATR multiplied by the ATR multiplier.
SMA Calculation: The 21-period SMA of the closing price is used as a trend filter.
Entry and Exit Conditions:
Long Entry: A long position is initiated when the closing price crosses over the low stop and is above the 21-period SMA. This condition ensures that the market is trending upward and that the entry is made in the direction of the prevailing trend.
Exit Long: The long position is exited when the closing price falls below the high stop, indicating potential downward movement and protecting against significant drawdowns.
Position Sizing:
The quantity of shares to trade is calculated based on the selected calculation mode (linear or exponential) and the risk multiplier. This ensures position size is adjusted dynamically based on current market conditions and user-defined risk tolerance.
Exponential Mode: Quantity is calculated using the formula: riskMultiplier / lowestClose * 1000 * strategy.equity / strategy.initial_capital.
Linear Mode: Quantity is calculated using the formula: riskMultiplier / lowestClose * 1000.
Execution:
When the long entry condition is met, the strategy triggers a buy signal, and a long position is entered with the calculated quantity. An alert is generated to notify the trader.
When the exit condition is met, the strategy closes the position and triggers a sell signal, accompanied by an alert.
Plotting:
Buy Signals: Indicated with an upward triangle below the bar.
Sell Signals: Indicated with a downward triangle above the bar.
Application
This strategy is particularly effective for trading the SPX on a 1-hour timeframe, capitalizing on price movements by adjusting stop levels dynamically based on market volatility and trend direction.
Default Setup
Initial Capital: $1,000
Risk Multiplier: 5
ATR Period: 10
ATR Multiplier: 3
Stop Length: 21
SMA Length: 21
Commission: 0.01
Slippage: 3 Ticks
Backtesting Results
Backtesting indicates that the "Chande Kroll Stop Strategy" performs optimally on the SPX when applied to the 1-hour timeframe. The strategy's dynamic adjustment of stop levels helps manage risk effectively while capturing significant upward price movements. Backtesting was conducted with a realistic initial capital of $1,000, and commissions and slippage were included to ensure the results are not misleading.
Risk Management
The strategy incorporates risk management through dynamically calculated stop levels based on the ATR and a user-defined risk multiplier. This approach ensures that position sizes are adjusted according to market volatility, helping to mitigate potential losses. Trades are sized to risk a sustainable amount of equity, adhering to the guideline of risking no more than 5-10% per trade.
Usage Notes
Customization: Users can adjust the ATR period, ATR multiplier, stop length, and SMA length to better suit their trading style and risk tolerance.
Alerts: The strategy includes alerts for buy and sell signals to keep traders informed of potential entry and exit points.
Pyramiding: Although possible, the strategy yields the best results without pyramiding.
Justification of Components
The Chande Kroll Stop indicator and the 21-period SMA are combined to provide a robust framework for identifying long trading opportunities in trending markets. Here is why they work well together:
Chande Kroll Stop Indicator: This indicator provides dynamic stop levels that adapt to market volatility, allowing traders to set logical stop-loss levels that account for current price movements. It is particularly useful in volatile markets where fixed stops can be easily hit by random price fluctuations. By using the ATR, the stop levels adjust based on recent market activity, ensuring they remain relevant in varying market conditions.
21-Period SMA: The 21-period SMA acts as a trend filter to ensure trades are taken in the direction of the prevailing market trend. By requiring the closing price to be above the SMA for long entries, the strategy aligns itself with the broader market trend, reducing the risk of entering trades against the overall market direction. This helps to avoid false signals and ensures that the trades are in line with the dominant market movement.
Combining these two components creates a balanced approach that captures trending price movements while protecting against significant drawdowns through adaptive stop levels. The Chande Kroll Stop ensures that the stops are placed at levels that reflect current volatility, while the SMA filter ensures that trades are only taken when the market is trending in the desired direction.
Concepts Underlying Calculations
ATR (Average True Range): Used to measure market volatility, which informs the stop levels.
SMA (Simple Moving Average): Used to filter trades, ensuring positions are taken in the direction of the trend.
Chande Kroll Stop: Combines high and low price levels with ATR to create dynamic stop levels that adapt to market conditions.
Risk Disclaimer
Trading involves substantial risk, and most day traders incur losses. The "Chande Kroll Stop Strategy" is provided for informational and educational purposes only. Past performance is not indicative of future results. Users are advised to adjust and personalize this trading strategy to better match their individual trading preferences and risk tolerance.
Softmax Normalized T3 Histogram [Loxx]Softmax Normalized T3 Histogram is a T3 moving average that is morphed into a normalized oscillator from -1 to 1.
What is the Softmax function?
The softmax function, also known as softargmax: or normalized exponential function, converts a vector of K real numbers into a probability distribution of K possible outcomes. It is a generalization of the logistic function to multiple dimensions, and used in multinomial logistic regression. The softmax function is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes, based on Luce's choice axiom.
What is the T3 moving average?
Better Moving Averages Tim Tillson
November 1, 1998
Tim Tillson is a software project manager at Hewlett-Packard, with degrees in Mathematics and Computer Science. He has privately traded options and equities for 15 years.
Introduction
"Digital filtering includes the process of smoothing, predicting, differentiating, integrating, separation of signals, and removal of noise from a signal. Thus many people who do such things are actually using digital filters without realizing that they are; being unacquainted with the theory, they neither understand what they have done nor the possibilities of what they might have done."
This quote from R. W. Hamming applies to the vast majority of indicators in technical analysis . Moving averages, be they simple, weighted, or exponential, are lowpass filters; low frequency components in the signal pass through with little attenuation, while high frequencies are severely reduced.
"Oscillator" type indicators (such as MACD , Momentum, Relative Strength Index ) are another type of digital filter called a differentiator.
Tushar Chande has observed that many popular oscillators are highly correlated, which is sensible because they are trying to measure the rate of change of the underlying time series, i.e., are trying to be the first and second derivatives we all learned about in Calculus.
We use moving averages (lowpass filters) in technical analysis to remove the random noise from a time series, to discern the underlying trend or to determine prices at which we will take action. A perfect moving average would have two attributes:
It would be smooth, not sensitive to random noise in the underlying time series. Another way of saying this is that its derivative would not spuriously alternate between positive and negative values.
It would not lag behind the time series it is computed from. Lag, of course, produces late buy or sell signals that kill profits.
The only way one can compute a perfect moving average is to have knowledge of the future, and if we had that, we would buy one lottery ticket a week rather than trade!
Having said this, we can still improve on the conventional simple, weighted, or exponential moving averages. Here's how:
Two Interesting Moving Averages
We will examine two benchmark moving averages based on Linear Regression analysis.
In both cases, a Linear Regression line of length n is fitted to price data.
I call the first moving average ILRS, which stands for Integral of Linear Regression Slope. One simply integrates the slope of a linear regression line as it is successively fitted in a moving window of length n across the data, with the constant of integration being a simple moving average of the first n points. Put another way, the derivative of ILRS is the linear regression slope. Note that ILRS is not the same as a SMA ( simple moving average ) of length n, which is actually the midpoint of the linear regression line as it moves across the data.
We can measure the lag of moving averages with respect to a linear trend by computing how they behave when the input is a line with unit slope. Both SMA (n) and ILRS(n) have lag of n/2, but ILRS is much smoother than SMA .
Our second benchmark moving average is well known, called EPMA or End Point Moving Average. It is the endpoint of the linear regression line of length n as it is fitted across the data. EPMA hugs the data more closely than a simple or exponential moving average of the same length. The price we pay for this is that it is much noisier (less smooth) than ILRS, and it also has the annoying property that it overshoots the data when linear trends are present.
However, EPMA has a lag of 0 with respect to linear input! This makes sense because a linear regression line will fit linear input perfectly, and the endpoint of the LR line will be on the input line.
These two moving averages frame the tradeoffs that we are facing. On one extreme we have ILRS, which is very smooth and has considerable phase lag. EPMA has 0 phase lag, but is too noisy and overshoots. We would like to construct a better moving average which is as smooth as ILRS, but runs closer to where EPMA lies, without the overshoot.
A easy way to attempt this is to split the difference, i.e. use (ILRS(n)+EPMA(n))/2. This will give us a moving average (call it IE /2) which runs in between the two, has phase lag of n/4 but still inherits considerable noise from EPMA. IE /2 is inspirational, however. Can we build something that is comparable, but smoother? Figure 1 shows ILRS, EPMA, and IE /2.
Filter Techniques
Any thoughtful student of filter theory (or resolute experimenter) will have noticed that you can improve the smoothness of a filter by running it through itself multiple times, at the cost of increasing phase lag.
There is a complementary technique (called twicing by J.W. Tukey) which can be used to improve phase lag. If L stands for the operation of running data through a low pass filter, then twicing can be described by:
L' = L(time series) + L(time series - L(time series))
That is, we add a moving average of the difference between the input and the moving average to the moving average. This is algebraically equivalent to:
2L-L(L)
This is the Double Exponential Moving Average or DEMA , popularized by Patrick Mulloy in TASAC (January/February 1994).
In our taxonomy, DEMA has some phase lag (although it exponentially approaches 0) and is somewhat noisy, comparable to IE /2 indicator.
We will use these two techniques to construct our better moving average, after we explore the first one a little more closely.
Fixing Overshoot
An n-day EMA has smoothing constant alpha=2/(n+1) and a lag of (n-1)/2.
Thus EMA (3) has lag 1, and EMA (11) has lag 5. Figure 2 shows that, if I am willing to incur 5 days of lag, I get a smoother moving average if I run EMA (3) through itself 5 times than if I just take EMA (11) once.
This suggests that if EPMA and DEMA have 0 or low lag, why not run fast versions (eg DEMA (3)) through themselves many times to achieve a smooth result? The problem is that multiple runs though these filters increase their tendency to overshoot the data, giving an unusable result. This is because the amplitude response of DEMA and EPMA is greater than 1 at certain frequencies, giving a gain of much greater than 1 at these frequencies when run though themselves multiple times. Figure 3 shows DEMA (7) and EPMA(7) run through themselves 3 times. DEMA^3 has serious overshoot, and EPMA^3 is terrible.
The solution to the overshoot problem is to recall what we are doing with twicing:
DEMA (n) = EMA (n) + EMA (time series - EMA (n))
The second term is adding, in effect, a smooth version of the derivative to the EMA to achieve DEMA . The derivative term determines how hot the moving average's response to linear trends will be. We need to simply turn down the volume to achieve our basic building block:
EMA (n) + EMA (time series - EMA (n))*.7;
This is algebraically the same as:
EMA (n)*1.7-EMA( EMA (n))*.7;
I have chosen .7 as my volume factor, but the general formula (which I call "Generalized Dema") is:
GD (n,v) = EMA (n)*(1+v)-EMA( EMA (n))*v,
Where v ranges between 0 and 1. When v=0, GD is just an EMA , and when v=1, GD is DEMA . In between, GD is a cooler DEMA . By using a value for v less than 1 (I like .7), we cure the multiple DEMA overshoot problem, at the cost of accepting some additional phase delay. Now we can run GD through itself multiple times to define a new, smoother moving average T3 that does not overshoot the data:
T3(n) = GD ( GD ( GD (n)))
In filter theory parlance, T3 is a six-pole non-linear Kalman filter. Kalman filters are ones which use the error (in this case (time series - EMA (n)) to correct themselves. In Technical Analysis , these are called Adaptive Moving Averages; they track the time series more aggressively when it is making large moves.
Included:
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
T3 PPO [Loxx]T3 PPO is a percentage price oscillator indicator using T3 moving average. This indicator is used to spot reversals. Dark red is upward price exhaustion, dark green is downward price exhaustion.
What is Percentage Price Oscillator (PPO)?
The percentage price oscillator (PPO) is a technical momentum indicator that shows the relationship between two moving averages in percentage terms. The moving averages are a 26-period and 12-period exponential moving average (EMA).
The PPO is used to compare asset performance and volatility, spot divergence that could lead to price reversals, generate trade signals, and help confirm trend direction.
What is the T3 moving average?
Better Moving Averages Tim Tillson
November 1, 1998
Tim Tillson is a software project manager at Hewlett-Packard, with degrees in Mathematics and Computer Science. He has privately traded options and equities for 15 years.
Introduction
"Digital filtering includes the process of smoothing, predicting, differentiating, integrating, separation of signals, and removal of noise from a signal. Thus many people who do such things are actually using digital filters without realizing that they are; being unacquainted with the theory, they neither understand what they have done nor the possibilities of what they might have done."
This quote from R. W. Hamming applies to the vast majority of indicators in technical analysis . Moving averages, be they simple, weighted, or exponential, are lowpass filters; low frequency components in the signal pass through with little attenuation, while high frequencies are severely reduced.
"Oscillator" type indicators (such as MACD , Momentum, Relative Strength Index ) are another type of digital filter called a differentiator.
Tushar Chande has observed that many popular oscillators are highly correlated, which is sensible because they are trying to measure the rate of change of the underlying time series, i.e., are trying to be the first and second derivatives we all learned about in Calculus.
We use moving averages (lowpass filters) in technical analysis to remove the random noise from a time series, to discern the underlying trend or to determine prices at which we will take action. A perfect moving average would have two attributes:
It would be smooth, not sensitive to random noise in the underlying time series. Another way of saying this is that its derivative would not spuriously alternate between positive and negative values.
It would not lag behind the time series it is computed from. Lag, of course, produces late buy or sell signals that kill profits.
The only way one can compute a perfect moving average is to have knowledge of the future, and if we had that, we would buy one lottery ticket a week rather than trade!
Having said this, we can still improve on the conventional simple, weighted, or exponential moving averages. Here's how:
Two Interesting Moving Averages
We will examine two benchmark moving averages based on Linear Regression analysis.
In both cases, a Linear Regression line of length n is fitted to price data.
I call the first moving average ILRS, which stands for Integral of Linear Regression Slope. One simply integrates the slope of a linear regression line as it is successively fitted in a moving window of length n across the data, with the constant of integration being a simple moving average of the first n points. Put another way, the derivative of ILRS is the linear regression slope. Note that ILRS is not the same as a SMA ( simple moving average ) of length n, which is actually the midpoint of the linear regression line as it moves across the data.
We can measure the lag of moving averages with respect to a linear trend by computing how they behave when the input is a line with unit slope. Both SMA (n) and ILRS(n) have lag of n/2, but ILRS is much smoother than SMA .
Our second benchmark moving average is well known, called EPMA or End Point Moving Average. It is the endpoint of the linear regression line of length n as it is fitted across the data. EPMA hugs the data more closely than a simple or exponential moving average of the same length. The price we pay for this is that it is much noisier (less smooth) than ILRS, and it also has the annoying property that it overshoots the data when linear trends are present.
However, EPMA has a lag of 0 with respect to linear input! This makes sense because a linear regression line will fit linear input perfectly, and the endpoint of the LR line will be on the input line.
These two moving averages frame the tradeoffs that we are facing. On one extreme we have ILRS, which is very smooth and has considerable phase lag. EPMA has 0 phase lag, but is too noisy and overshoots. We would like to construct a better moving average which is as smooth as ILRS, but runs closer to where EPMA lies, without the overshoot.
A easy way to attempt this is to split the difference, i.e. use (ILRS(n)+EPMA(n))/2. This will give us a moving average (call it IE /2) which runs in between the two, has phase lag of n/4 but still inherits considerable noise from EPMA. IE /2 is inspirational, however. Can we build something that is comparable, but smoother? Figure 1 shows ILRS, EPMA, and IE /2.
Filter Techniques
Any thoughtful student of filter theory (or resolute experimenter) will have noticed that you can improve the smoothness of a filter by running it through itself multiple times, at the cost of increasing phase lag.
There is a complementary technique (called twicing by J.W. Tukey) which can be used to improve phase lag. If L stands for the operation of running data through a low pass filter, then twicing can be described by:
L' = L(time series) + L(time series - L(time series))
That is, we add a moving average of the difference between the input and the moving average to the moving average. This is algebraically equivalent to:
2L-L(L)
This is the Double Exponential Moving Average or DEMA , popularized by Patrick Mulloy in TASAC (January/February 1994).
In our taxonomy, DEMA has some phase lag (although it exponentially approaches 0) and is somewhat noisy, comparable to IE /2 indicator.
We will use these two techniques to construct our better moving average, after we explore the first one a little more closely.
Fixing Overshoot
An n-day EMA has smoothing constant alpha=2/(n+1) and a lag of (n-1)/2.
Thus EMA (3) has lag 1, and EMA (11) has lag 5. Figure 2 shows that, if I am willing to incur 5 days of lag, I get a smoother moving average if I run EMA (3) through itself 5 times than if I just take EMA (11) once.
This suggests that if EPMA and DEMA have 0 or low lag, why not run fast versions (eg DEMA (3)) through themselves many times to achieve a smooth result? The problem is that multiple runs though these filters increase their tendency to overshoot the data, giving an unusable result. This is because the amplitude response of DEMA and EPMA is greater than 1 at certain frequencies, giving a gain of much greater than 1 at these frequencies when run though themselves multiple times. Figure 3 shows DEMA (7) and EPMA(7) run through themselves 3 times. DEMA^3 has serious overshoot, and EPMA^3 is terrible.
The solution to the overshoot problem is to recall what we are doing with twicing:
DEMA (n) = EMA (n) + EMA (time series - EMA (n))
The second term is adding, in effect, a smooth version of the derivative to the EMA to achieve DEMA . The derivative term determines how hot the moving average's response to linear trends will be. We need to simply turn down the volume to achieve our basic building block:
EMA (n) + EMA (time series - EMA (n))*.7;
This is algebraically the same as:
EMA (n)*1.7-EMA( EMA (n))*.7;
I have chosen .7 as my volume factor, but the general formula (which I call "Generalized Dema") is:
GD (n,v) = EMA (n)*(1+v)-EMA( EMA (n))*v,
Where v ranges between 0 and 1. When v=0, GD is just an EMA , and when v=1, GD is DEMA . In between, GD is a cooler DEMA . By using a value for v less than 1 (I like .7), we cure the multiple DEMA overshoot problem, at the cost of accepting some additional phase delay. Now we can run GD through itself multiple times to define a new, smoother moving average T3 that does not overshoot the data:
T3(n) = GD ( GD ( GD (n)))
In filter theory parlance, T3 is a six-pole non-linear Kalman filter. Kalman filters are ones which use the error (in this case (time series - EMA (n)) to correct themselves. In Technical Analysis , these are called Adaptive Moving Averages; they track the time series more aggressively when it is making large moves.
Auto-Fit Growth Trendline# **Theoretical Algorithmic Principles of the Auto-Fit Growth Trendline (AFGT)**
## **🎯 What Does This Algorithm Do?**
The Auto-Fit Growth Trendline is an advanced technical analysis system that **automates the identification of long-term growth trends** and **projects future price levels** based on historical cyclical patterns.
### **Primary Functionality:**
- **Automatically detects** the most significant lows in regular periods (monthly, quarterly, semi-annually, annually)
- **Constructs a dynamic trendline** that connects these historical lows
- **Projects the trend into the future** with high mathematical precision
- **Generates Fibonacci bands** that act as dynamic support and resistance levels
- **Automatically adapts** to different timeframes and market conditions
### **Strategic Purpose:**
The algorithm is designed to identify **fundamental value zones** where price has historically found support, enabling traders to:
- Identify optimal entry points for long positions
- Establish realistic price targets based on mathematical projections
- Recognize dynamic support and resistance levels
- Anticipate long-term price movements
---
## **🧮 Core Mathematical Foundations**
### **Adaptive Temporal Segmentation Theory**
The algorithm is based on **dynamic temporal partition theory**, where time is divided into mathematically coherent uniform intervals. It uses modular transformations to create bijective mappings between continuous timestamps and discrete periods, ensuring each temporal point belongs uniquely to a specific period.
**What does this achieve?** It allows the algorithm to automatically identify natural market cycles (annual, quarterly, etc.) without manual intervention, adapting to the inherent periodicity of each asset.
The temporal mapping function implements a **discrete affine transformation** that normalizes different frequencies (monthly, quarterly, semi-annual, annual) to a space of unique identifiers, enabling consistent cross-temporal comparative analysis.
---
## **📊 Local Extrema Detection Theory**
### **Multi-Point Retrospective Validation Principle**
Local minima detection is founded on **relative extrema theory with sliding window**. Instead of using a simple minimum finder, it implements a cross-validation system that examines the persistence of the extremum across multiple historical periods.
**What problem does this solve?** It eliminates false minima caused by temporal volatility, identifying only those points that represent true historical support levels with statistical significance.
This approach is based on the **statistical confirmation principle**, where a minimum is only considered valid if it maintains its extremum condition during a defined observation period, significantly reducing false positives caused by transitory volatility.
---
## **🔬 Robust Interpolation Theory with Outlier Control**
### **Contextual Adaptive Interpolation Model**
The mathematical core uses **piecewise linear interpolation with adaptive outlier correction**. The key innovation lies in implementing a **contextual anomaly detector** that identifies not only absolute extreme values, but relative deviations to the local context.
**Why is this important?** Financial markets contain extreme events (crashes, bubbles) that can distort projections. This system identifies and appropriately weights them without completely eliminating them, preserving directional information while attenuating distortions.
### **Implicit Bayesian Smoothing Algorithm**
When an outlier is detected (deviation >300% of local average), the system applies a **simplified Kalman filter** that combines the current observation with a local trend estimation, using a weight factor that preserves directional information while attenuating extreme fluctuations.
---
## **📈 Stabilized Extrapolation Theory**
### **Exponential Growth Model with Dampening**
Extrapolation is based on a **modified exponential growth model with progressive dampening**. It uses multiple historical points to calculate local growth ratios, implements statistical filtering to eliminate outliers, and applies a dampening factor that increases with extrapolation distance.
**What advantage does this offer?** Long-term projections in finance tend to be exponentially unrealistic. This system maintains short-to-medium term accuracy while converging toward realistic long-term projections, avoiding the typical "exponential explosions" of other methods.
### **Asymptotic Convergence Principle**
For long-term projections, the algorithm implements **controlled asymptotic convergence**, where growth ratios gradually converge toward pre-established limits, avoiding unrealistic exponential projections while preserving short-to-medium term accuracy.
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## **🌟 Dynamic Fibonacci Projection Theory**
### **Continuous Proportional Scaling Model**
Fibonacci bands are constructed through **uniform proportional scaling** of the base curve, where each level represents a linear transformation of the main curve by a constant factor derived from the Fibonacci sequence.
**What is its practical utility?** It provides dynamic resistance and support levels that move with the trend, offering price targets and profit-taking points that automatically adapt to market evolution.
### **Topological Preservation Principle**
The system maintains the **topological properties** of the base curve in all Fibonacci projections, ensuring that spatial and temporal relationships are consistently preserved across all resistance/support levels.
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## **⚡ Adaptive Computational Optimization**
### **Multi-Scale Resolution Theory**
It implements **automatic multi-resolution analysis** where data granularity is dynamically adjusted according to the analysis timeframe. It uses the **adaptive Nyquist principle** to optimize the signal-to-noise ratio according to the temporal observation scale.
**Why is this necessary?** Different timeframes require different levels of detail. A 1-minute chart needs more granularity than a monthly one. This system automatically optimizes resolution for each case.
### **Adaptive Density Algorithm**
Calculation point density is optimized through **adaptive sampling theory**, where calculation frequency is adjusted according to local trend curvature and analysis timeframe, balancing visual precision with computational efficiency.
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## **🛡️ Robustness and Fault Tolerance**
### **Graceful Degradation Theory**
The system implements **multi-level graceful degradation**, where under error conditions or insufficient data, the algorithm progressively falls back to simpler but reliable methods, maintaining basic functionality under any condition.
**What does this guarantee?** That the indicator functions consistently even with incomplete data, new symbols with limited history, or extreme market conditions.
### **State Consistency Principle**
It uses **mathematical invariants** to guarantee that the algorithm's internal state remains consistent between executions, implementing consistency checks that validate data structure integrity in each iteration.
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## **🔍 Key Theoretical Innovations**
### **A. Contextual vs. Absolute Outlier Detection**
It revolutionizes traditional outlier detection by considering not only the absolute magnitude of deviations, but their relative significance within the local context of the time series.
**Practical impact:** It distinguishes between legitimate market movements and technical anomalies, preserving important events like breakouts while filtering noise.
### **B. Extrapolation with Weighted Historical Memory**
It implements a memory system that weights different historical periods according to their relevance for current prediction, creating projections more adaptable to market regime changes.
**Competitive advantage:** It automatically adapts to fundamental changes in asset dynamics without requiring manual recalibration.
### **C. Automatic Multi-Timeframe Adaptation**
It develops an automatic temporal resolution selection system that optimizes signal extraction according to the intrinsic characteristics of the analysis timeframe.
**Result:** A single indicator that functions optimally from 1-minute to monthly charts without manual adjustments.
### **D. Intelligent Asymptotic Convergence**
It introduces the concept of controlled asymptotic convergence in financial extrapolations, where long-term projections converge toward realistic limits based on historical fundamentals.
**Added value:** Mathematically sound long-term projections that avoid the unrealistic extremes typical of other extrapolation methods.
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## **📊 Complexity and Scalability Theory**
### **Optimized Linear Complexity Model**
The algorithm maintains **linear computational complexity** O(n) in the number of historical data points, guaranteeing scalability for extensive time series analysis without performance degradation.
### **Temporal Locality Principle**
It implements **temporal locality**, where the most expensive operations are concentrated in the most relevant temporal regions (recent periods and near projections), optimizing computational resource usage.
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## **🎯 Convergence and Stability**
### **Probabilistic Convergence Theory**
The system guarantees **probabilistic convergence** toward the real underlying trend, where projection accuracy increases with the amount of available historical data, following **law of large numbers** principles.
**Practical implication:** The more history an asset has, the more accurate the algorithm's projections will be.
### **Guaranteed Numerical Stability**
It implements **intrinsic numerical stability** through the use of robust floating-point arithmetic and validations that prevent overflow, underflow, and numerical error propagation.
**Result:** Reliable operation even with extreme-priced assets (from satoshis to thousand-dollar stocks).
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## **💼 Comprehensive Practical Application**
**The algorithm functions as a "financial GPS"** that:
1. **Identifies where we've been** (significant historical lows)
2. **Determines where we are** (current position relative to the trend)
3. **Projects where we're going** (future trend with specific price levels)
4. **Provides alternative routes** (Fibonacci bands as alternative targets)
This theoretical framework represents an innovative synthesis of time series analysis, approximation theory, and computational optimization, specifically designed for long-term financial trend analysis with robust and mathematically grounded projections.
