Cerca negli script per "Exponential"
EMA FIBO 4HOURSExponential Moving Averages of 4 Fibonacci Levels((55,144,233,377)*6) in 4 Hour Timezone
EMA Cross x3 (7, 77, 231)Exponential Moving Average at periods, 7, 77, 231. You will see a blue cross when the short EMA crosses the medium EMA, and a green cross when it crosses the long EMA.
EMA SpreadExponential Moving Average Spread is the percentage spread difference between EMA1 (Slow) and EMA2 (Fast) ie. the gap between two indicators slow and fast. Useful when used alongside EMA cross, MACD, and RSI to strengthen buy/sell signals.
MTF EMAExponential Moving Average indicator that can be configured to display different timeframe EMA's.
Timeframe is set in minutes. Max timeframe currently is the daily (1440 minutes). Any value higher than 1440 will result in no plot.
Examples:
Daily 50 EMA plotted on 4H chart
4H 50 EMA and Daily 50 EMA plotted on 1H chart
Can also work in reverse if needed.
Example, Daily 50 EMA plotted on Weekly Chart
[RS]Average Advance and Decline Curved Lines V0exponential curve linear regression, use falloff multiplier to control curve falloff strength.
4 Fibonacci EMAsAdd 4 Fibonacci EMAs to your charts with one indicator.
Configureable by value, so they don't necessarily have to use Fibonacci numbers, and by colors.
ONE RING 8 MA Bands with RaysCycle analysis tool ...
MAs: Eight moving averages (MA1–MA8) with customizable lengths, types (RMA, WMA, EMA, SMA), and offsets
Bands: Upper/lower bands for each MA, calculated based on final_pctX (Percentage mode) or final_ptsX (Points mode), scaled by multiplier
Rays: Forward-projected lines for bands, with customizable start points, styles (Solid, Dashed, Dotted), and lengths (up to 500 bars)
Band Choices
Manual: Uses individual inputs for band offsets
Uniform: Sets all offsets to base_pct (e.g., 0.1%) or base_pts (e.g., 0.1 points)
Linear: Scales linearly (e.g., base_pct * 1, base_pct * 2, base_pct * 3 ..., base_pct * 8)
Exponential: Scales exponentially (e.g., base_pct * 1, base_pct * 2, base_pct * 4, base_pct * 8 ..., base_pct * 128)
ATR-Based: Offsets are derived from the Average True Range (ATR), scaled by a linear factor. Dynamic bands that adapt to market conditions, useful for breakout or mean-reversion strategies. (final_pct1 = base_pct * atr, final_pct2 = base_pct * atr * 2, ..., final_pct8 = base_pct * atr * 8)
Geometric: Offsets follow a geometric progression (e.g., base_pct * r^0, base_pct * r^1, base_pct * r^2, ..., where r is a ratio like 1.5) This is less aggressive than Exponential (which uses powers of 2) and provides a smoother progression.
Example: If base_pct = 0.1, r = 1.5, then final_pct1 = 0.1%, final_pct2 = 0.15%, final_pct3 = 0.225%, ..., final_pct8 ≈ 1.71%
Harmonic: Offsets are based on harmonic flavored ratios. final_pctX = base_pct * X / (9 - X), final_ptsX = base_pts * X / (9 - X) for X = 1 to 8 This creates a harmonic-like progression where offsets increase non-linearly, ensuring MA8 bands are wider than MA1 bands, and avoids duplicating the Linear choice above.
Ex. offsets for base_pct = 0.1: MA1: ±0.0125% (0.1 * 1/8), MA2: ±0.0286% (0.1 * 2/7), MA3: ±0.05% (0.1 * 3/6), MA4: ±0.08% (0.1 * 4/5), MA5: ±0.125% (0.1 * 5/4), MA6: ±0.2% (0.1 * 6/3), MA7: ±0.35% (0.1 * 7/2), MA8: ±0.8% (0.1 * 8/1)
Square Root: Offsets grow with the square root of the band index (e.g., base_pct * sqrt(1), base_pct * sqrt(2), ..., base_pct * sqrt(8)). This creates a gradual widening, less aggressive than Linear or Exponential. Set final_pct1 = base_pct * sqrt(1), final_pct2 = base_pct * sqrt(2), ..., final_pct8 = base_pct * sqrt(8).
Example: If base_pct = 0.1, then final_pct1 = 0.1%, final_pct2 ≈ 0.141%, final_pct3 ≈ 0.173%, ..., final_pct8 ≈ 0.283%.
Fibonacci: Uses Fibonacci ratios (e.g., base_pct * 1, base_pct * 1.618, base_pct * 2.618
Percentage vs. Points Toggle:
In Percentage mode, bands are calculated as ma * (1 ± (final_pct / 100) * multiplier)
In Points mode, bands are calculated as ma ± final_pts * multiplier, where final_pts is in price units.
Threshold Setting for Slope:
Threshold setting for determining when the slope would be significant enough to call it a change in direction. Can check efficiency by setting MA1 to color on slope temporarily
Arrow table: Shows slope direction of 8 MAs using an Up or Down triangle, or shows Flat condition if no triangle.
taLibrary "ta"
█ OVERVIEW
This library holds technical analysis functions calculating values for which no Pine built-in exists.
Look first. Then leap.
█ FUNCTIONS
cagr(entryTime, entryPrice, exitTime, exitPrice)
It calculates the "Compound Annual Growth Rate" between two points in time. The CAGR is a notional, annualized growth rate that assumes all profits are reinvested. It only takes into account the prices of the two end points — not drawdowns, so it does not calculate risk. It can be used as a yardstick to compare the performance of two instruments. Because it annualizes values, the function requires a minimum of one day between the two end points (annualizing returns over smaller periods of times doesn't produce very meaningful figures).
Parameters:
entryTime : The starting timestamp.
entryPrice : The starting point's price.
exitTime : The ending timestamp.
exitPrice : The ending point's price.
Returns: CAGR in % (50 is 50%). Returns `na` if there is not >=1D between `entryTime` and `exitTime`, or until the two time points have not been reached by the script.
█ v2, Mar. 8, 2022
Added functions `allTimeHigh()` and `allTimeLow()` to find the highest or lowest value of a source from the first historical bar to the current bar. These functions will not look ahead; they will only return new highs/lows on the bar where they occur.
allTimeHigh(src)
Tracks the highest value of `src` from the first historical bar to the current bar.
Parameters:
src : (series int/float) Series to track. Optional. The default is `high`.
Returns: (float) The highest value tracked.
allTimeLow(src)
Tracks the lowest value of `src` from the first historical bar to the current bar.
Parameters:
src : (series int/float) Series to track. Optional. The default is `low`.
Returns: (float) The lowest value tracked.
█ v3, Sept. 27, 2022
This version includes the following new functions:
aroon(length)
Calculates the values of the Aroon indicator.
Parameters:
length (simple int) : (simple int) Number of bars (length).
Returns: ( [float, float ]) A tuple of the Aroon-Up and Aroon-Down values.
coppock(source, longLength, shortLength, smoothLength)
Calculates the value of the Coppock Curve indicator.
Parameters:
source (float) : (series int/float) Series of values to process.
longLength (simple int) : (simple int) Number of bars for the fast ROC value (length).
shortLength (simple int) : (simple int) Number of bars for the slow ROC value (length).
smoothLength (simple int) : (simple int) Number of bars for the weigted moving average value (length).
Returns: (float) The oscillator value.
dema(source, length)
Calculates the value of the Double Exponential Moving Average (DEMA).
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Length for the smoothing parameter calculation.
Returns: (float) The double exponentially weighted moving average of the `source`.
dema2(src, length)
An alternate Double Exponential Moving Average (Dema) function to `dema()`, which allows a "series float" length argument.
Parameters:
src : (series int/float) Series of values to process.
length : (series int/float) Length for the smoothing parameter calculation.
Returns: (float) The double exponentially weighted moving average of the `src`.
dm(length)
Calculates the value of the "Demarker" indicator.
Parameters:
length (simple int) : (simple int) Number of bars (length).
Returns: (float) The oscillator value.
donchian(length)
Calculates the values of a Donchian Channel using `high` and `low` over a given `length`.
Parameters:
length (int) : (series int) Number of bars (length).
Returns: ( [float, float, float ]) A tuple containing the channel high, low, and median, respectively.
ema2(src, length)
An alternate ema function to the `ta.ema()` built-in, which allows a "series float" length argument.
Parameters:
src : (series int/float) Series of values to process.
length : (series int/float) Number of bars (length).
Returns: (float) The exponentially weighted moving average of the `src`.
eom(length, div)
Calculates the value of the Ease of Movement indicator.
Parameters:
length (simple int) : (simple int) Number of bars (length).
div (simple int) : (simple int) Divisor used for normalzing values. Optional. The default is 10000.
Returns: (float) The oscillator value.
frama(source, length)
The Fractal Adaptive Moving Average (FRAMA), developed by John Ehlers, is an adaptive moving average that dynamically adjusts its lookback period based on fractal geometry.
Parameters:
source (float) : (series int/float) Series of values to process.
length (int) : (series int) Number of bars (length).
Returns: (float) The fractal adaptive moving average of the `source`.
ft(source, length)
Calculates the value of the Fisher Transform indicator.
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Number of bars (length).
Returns: (float) The oscillator value.
ht(source)
Calculates the value of the Hilbert Transform indicator.
Parameters:
source (float) : (series int/float) Series of values to process.
Returns: (float) The oscillator value.
ichimoku(conLength, baseLength, senkouLength)
Calculates values of the Ichimoku Cloud indicator, including tenkan, kijun, senkouSpan1, senkouSpan2, and chikou. NOTE: offsets forward or backward can be done using the `offset` argument in `plot()`.
Parameters:
conLength (int) : (series int) Length for the Conversion Line (Tenkan). The default is 9 periods, which returns the mid-point of the 9 period Donchian Channel.
baseLength (int) : (series int) Length for the Base Line (Kijun-sen). The default is 26 periods, which returns the mid-point of the 26 period Donchian Channel.
senkouLength (int) : (series int) Length for the Senkou Span 2 (Leading Span B). The default is 52 periods, which returns the mid-point of the 52 period Donchian Channel.
Returns: ( [float, float, float, float, float ]) A tuple of the Tenkan, Kijun, Senkou Span 1, Senkou Span 2, and Chikou Span values. NOTE: by default, the senkouSpan1 and senkouSpan2 should be plotted 26 periods in the future, and the Chikou Span plotted 26 days in the past.
ift(source)
Calculates the value of the Inverse Fisher Transform indicator.
Parameters:
source (float) : (series int/float) Series of values to process.
Returns: (float) The oscillator value.
kvo(fastLen, slowLen, trigLen)
Calculates the values of the Klinger Volume Oscillator.
Parameters:
fastLen (simple int) : (simple int) Length for the fast moving average smoothing parameter calculation.
slowLen (simple int) : (simple int) Length for the slow moving average smoothing parameter calculation.
trigLen (simple int) : (simple int) Length for the trigger moving average smoothing parameter calculation.
Returns: ( [float, float ]) A tuple of the KVO value, and the trigger value.
pzo(length)
Calculates the value of the Price Zone Oscillator.
Parameters:
length (simple int) : (simple int) Length for the smoothing parameter calculation.
Returns: (float) The oscillator value.
rms(source, length)
Calculates the Root Mean Square of the `source` over the `length`.
Parameters:
source (float) : (series int/float) Series of values to process.
length (int) : (series int) Number of bars (length).
Returns: (float) The RMS value.
rwi(length)
Calculates the values of the Random Walk Index.
Parameters:
length (simple int) : (simple int) Lookback and ATR smoothing parameter length.
Returns: ( [float, float ]) A tuple of the `rwiHigh` and `rwiLow` values.
stc(source, fast, slow, cycle, d1, d2)
Calculates the value of the Schaff Trend Cycle indicator.
Parameters:
source (float) : (series int/float) Series of values to process.
fast (simple int) : (simple int) Length for the MACD fast smoothing parameter calculation.
slow (simple int) : (simple int) Length for the MACD slow smoothing parameter calculation.
cycle (simple int) : (simple int) Number of bars for the Stochastic values (length).
d1 (simple int) : (simple int) Length for the initial %D smoothing parameter calculation.
d2 (simple int) : (simple int) Length for the final %D smoothing parameter calculation.
Returns: (float) The oscillator value.
stochFull(periodK, smoothK, periodD)
Calculates the %K and %D values of the Full Stochastic indicator.
Parameters:
periodK (simple int) : (simple int) Number of bars for Stochastic calculation. (length).
smoothK (simple int) : (simple int) Number of bars for smoothing of the %K value (length).
periodD (simple int) : (simple int) Number of bars for smoothing of the %D value (length).
Returns: ( [float, float ]) A tuple of the slow %K and the %D moving average values.
stochRsi(lengthRsi, periodK, smoothK, periodD, source)
Calculates the %K and %D values of the Stochastic RSI indicator.
Parameters:
lengthRsi (simple int) : (simple int) Length for the RSI smoothing parameter calculation.
periodK (simple int) : (simple int) Number of bars for Stochastic calculation. (length).
smoothK (simple int) : (simple int) Number of bars for smoothing of the %K value (length).
periodD (simple int) : (simple int) Number of bars for smoothing of the %D value (length).
source (float) : (series int/float) Series of values to process. Optional. The default is `close`.
Returns: ( [float, float ]) A tuple of the slow %K and the %D moving average values.
supertrend(factor, atrLength, wicks)
Calculates the values of the SuperTrend indicator with the ability to take candle wicks into account, rather than only the closing price.
Parameters:
factor (float) : (series int/float) Multiplier for the ATR value.
atrLength (simple int) : (simple int) Length for the ATR smoothing parameter calculation.
wicks (simple bool) : (simple bool) Condition to determine whether to take candle wicks into account when reversing trend, or to use the close price. Optional. Default is false.
Returns: ( [float, int ]) A tuple of the superTrend value and trend direction.
szo(source, length)
Calculates the value of the Sentiment Zone Oscillator.
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Length for the smoothing parameter calculation.
Returns: (float) The oscillator value.
t3(source, length, vf)
Calculates the value of the Tilson Moving Average (T3).
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Length for the smoothing parameter calculation.
vf (simple float) : (simple float) Volume factor. Affects the responsiveness.
Returns: (float) The Tilson moving average of the `source`.
t3Alt(source, length, vf)
An alternate Tilson Moving Average (T3) function to `t3()`, which allows a "series float" `length` argument.
Parameters:
source (float) : (series int/float) Series of values to process.
length (float) : (series int/float) Length for the smoothing parameter calculation.
vf (simple float) : (simple float) Volume factor. Affects the responsiveness.
Returns: (float) The Tilson moving average of the `source`.
tema(source, length)
Calculates the value of the Triple Exponential Moving Average (TEMA).
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Length for the smoothing parameter calculation.
Returns: (float) The triple exponentially weighted moving average of the `source`.
tema2(source, length)
An alternate Triple Exponential Moving Average (TEMA) function to `tema()`, which allows a "series float" `length` argument.
Parameters:
source (float) : (series int/float) Series of values to process.
length (float) : (series int/float) Length for the smoothing parameter calculation.
Returns: (float) The triple exponentially weighted moving average of the `source`.
trima(source, length)
Calculates the value of the Triangular Moving Average (TRIMA).
Parameters:
source (float) : (series int/float) Series of values to process.
length (int) : (series int) Number of bars (length).
Returns: (float) The triangular moving average of the `source`.
trima2(src, length)
An alternate Triangular Moving Average (TRIMA) function to `trima()`, which allows a "series int" length argument.
Parameters:
src : (series int/float) Series of values to process.
length : (series int) Number of bars (length).
Returns: (float) The triangular moving average of the `src`.
trix(source, length, signalLength, exponential)
Calculates the values of the TRIX indicator.
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Length for the smoothing parameter calculation.
signalLength (simple int) : (simple int) Length for smoothing the signal line.
exponential (simple bool) : (simple bool) Condition to determine whether exponential or simple smoothing is used. Optional. The default is `true` (exponential smoothing).
Returns: ( [float, float, float ]) A tuple of the TRIX value, the signal value, and the histogram.
uo(fastLen, midLen, slowLen)
Calculates the value of the Ultimate Oscillator.
Parameters:
fastLen (simple int) : (series int) Number of bars for the fast smoothing average (length).
midLen (simple int) : (series int) Number of bars for the middle smoothing average (length).
slowLen (simple int) : (series int) Number of bars for the slow smoothing average (length).
Returns: (float) The oscillator value.
vhf(source, length)
Calculates the value of the Vertical Horizontal Filter.
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Number of bars (length).
Returns: (float) The oscillator value.
vi(length)
Calculates the values of the Vortex Indicator.
Parameters:
length (simple int) : (simple int) Number of bars (length).
Returns: ( [float, float ]) A tuple of the viPlus and viMinus values.
vzo(length)
Calculates the value of the Volume Zone Oscillator.
Parameters:
length (simple int) : (simple int) Length for the smoothing parameter calculation.
Returns: (float) The oscillator value.
williamsFractal(period)
Detects Williams Fractals.
Parameters:
period (int) : (series int) Number of bars (length).
Returns: ( [bool, bool ]) A tuple of an up fractal and down fractal. Variables are true when detected.
wpo(length)
Calculates the value of the Wave Period Oscillator.
Parameters:
length (simple int) : (simple int) Length for the smoothing parameter calculation.
Returns: (float) The oscillator value.
█ v7, Nov. 2, 2023
This version includes the following new and updated functions:
atr2(length)
An alternate ATR function to the `ta.atr()` built-in, which allows a "series float" `length` argument.
Parameters:
length (float) : (series int/float) Length for the smoothing parameter calculation.
Returns: (float) The ATR value.
changePercent(newValue, oldValue)
Calculates the percentage difference between two distinct values.
Parameters:
newValue (float) : (series int/float) The current value.
oldValue (float) : (series int/float) The previous value.
Returns: (float) The percentage change from the `oldValue` to the `newValue`.
donchian(length)
Calculates the values of a Donchian Channel using `high` and `low` over a given `length`.
Parameters:
length (int) : (series int) Number of bars (length).
Returns: ( [float, float, float ]) A tuple containing the channel high, low, and median, respectively.
highestSince(cond, source)
Tracks the highest value of a series since the last occurrence of a condition.
Parameters:
cond (bool) : (series bool) A condition which, when `true`, resets the tracking of the highest `source`.
source (float) : (series int/float) Series of values to process. Optional. The default is `high`.
Returns: (float) The highest `source` value since the last time the `cond` was `true`.
lowestSince(cond, source)
Tracks the lowest value of a series since the last occurrence of a condition.
Parameters:
cond (bool) : (series bool) A condition which, when `true`, resets the tracking of the lowest `source`.
source (float) : (series int/float) Series of values to process. Optional. The default is `low`.
Returns: (float) The lowest `source` value since the last time the `cond` was `true`.
relativeVolume(length, anchorTimeframe, isCumulative, adjustRealtime)
Calculates the volume since the last change in the time value from the `anchorTimeframe`, the historical average volume using bars from past periods that have the same relative time offset as the current bar from the start of its period, and the ratio of these volumes. The volume values are cumulative by default, but can be adjusted to non-accumulated with the `isCumulative` parameter.
Parameters:
length (simple int) : (simple int) The number of periods to use for the historical average calculation.
anchorTimeframe (simple string) : (simple string) The anchor timeframe used in the calculation. Optional. Default is "D".
isCumulative (simple bool) : (simple bool) If `true`, the volume values will be accumulated since the start of the last `anchorTimeframe`. If `false`, values will be used without accumulation. Optional. The default is `true`.
adjustRealtime (simple bool) : (simple bool) If `true`, estimates the cumulative value on unclosed bars based on the data since the last `anchor` condition. Optional. The default is `false`.
Returns: ( [float, float, float ]) A tuple of three float values. The first element is the current volume. The second is the average of volumes at equivalent time offsets from past anchors over the specified number of periods. The third is the ratio of the current volume to the historical average volume.
rma2(source, length)
An alternate RMA function to the `ta.rma()` built-in, which allows a "series float" `length` argument.
Parameters:
source (float) : (series int/float) Series of values to process.
length (float) : (series int/float) Length for the smoothing parameter calculation.
Returns: (float) The rolling moving average of the `source`.
supertrend2(factor, atrLength, wicks)
An alternate SuperTrend function to `supertrend()`, which allows a "series float" `atrLength` argument.
Parameters:
factor (float) : (series int/float) Multiplier for the ATR value.
atrLength (float) : (series int/float) Length for the ATR smoothing parameter calculation.
wicks (simple bool) : (simple bool) Condition to determine whether to take candle wicks into account when reversing trend, or to use the close price. Optional. Default is `false`.
Returns: ( [float, int ]) A tuple of the superTrend value and trend direction.
vStop(source, atrLength, atrFactor)
Calculates an ATR-based stop value that trails behind the `source`. Can serve as a possible stop-loss guide and trend identifier.
Parameters:
source (float) : (series int/float) Series of values that the stop trails behind.
atrLength (simple int) : (simple int) Length for the ATR smoothing parameter calculation.
atrFactor (float) : (series int/float) The multiplier of the ATR value. Affects the maximum distance between the stop and the `source` value. A value of 1 means the maximum distance is 100% of the ATR value. Optional. The default is 1.
Returns: ( [float, bool ]) A tuple of the volatility stop value and the trend direction as a "bool".
vStop2(source, atrLength, atrFactor)
An alternate Volatility Stop function to `vStop()`, which allows a "series float" `atrLength` argument.
Parameters:
source (float) : (series int/float) Series of values that the stop trails behind.
atrLength (float) : (series int/float) Length for the ATR smoothing parameter calculation.
atrFactor (float) : (series int/float) The multiplier of the ATR value. Affects the maximum distance between the stop and the `source` value. A value of 1 means the maximum distance is 100% of the ATR value. Optional. The default is 1.
Returns: ( [float, bool ]) A tuple of the volatility stop value and the trend direction as a "bool".
Removed Functions:
allTimeHigh(src)
Tracks the highest value of `src` from the first historical bar to the current bar.
allTimeLow(src)
Tracks the lowest value of `src` from the first historical bar to the current bar.
trima2(src, length)
An alternate Triangular Moving Average (TRIMA) function to `trima()`, which allows a
"series int" length argument.
Why EMA Isn't What You Think It IsMany new traders adopt the Exponential Moving Average (EMA) believing it's simply a "better Simple Moving Average (SMA)". This common misconception leads to fundamental misunderstandings about how EMA works and when to use it.
EMA and SMA differ at their core. SMA use a window of finite number of data points, giving equal weight to each data point in the calculation period. This makes SMA a Finite Impulse Response (FIR) filter in signal processing terms. Remember that FIR means that "all that we need is the 'period' number of data points" to calculate the filter value. Anything beyond the given period is not relevant to FIR filters – much like how a security camera with 14-day storage automatically overwrites older footage, making last month's activity completely invisible regardless of how important it might have been.
EMA, however, is an Infinite Impulse Response (IIR) filter. It uses ALL historical data, with each past price having a diminishing - but never zero - influence on the calculated value. This creates an EMA response that extends infinitely into the past—not just for the last N periods. IIR filters cannot be precise if we give them only a 'period' number of data to work on - they will be off-target significantly due to lack of context, like trying to understand Game of Thrones by watching only the final season and wondering why everyone's so upset about that dragon lady going full pyromaniac.
If we only consider a number of data points equal to the EMA's period, we are capturing no more than 86.5% of the total weight of the EMA calculation. Relying on he period window alone (the warm-up period) will provide only 1 - (1 / e^2) weights, which is approximately 1−0.1353 = 0.8647 = 86.5%. That's like claiming you've read a book when you've skipped the first few chapters – technically, you got most of it, but you probably miss some crucial early context.
▶️ What is period in EMA used for?
What does a period parameter really mean for EMA? When we select a 15-period EMA, we're not selecting a window of 15 data points as with an SMA. Instead, we are using that number to calculate a decay factor (α) that determines how quickly older data loses influence in EMA result. Every trader knows EMA calculation: α = 1 / (1+period) – or at least every trader claims to know this while secretly checking the formula when they need it.
Thinking in terms of "period" seriously restricts EMA. The α parameter can be - should be! - any value between 0.0 and 1.0, offering infinite tuning possibilities of the indicator. When we limit ourselves to whole-number periods that we use in FIR indicators, we can only access a small subset of possible IIR calculations – it's like having access to the entire RGB color spectrum with 16.7 million possible colors but stubbornly sticking to the 8 basic crayons in a child's first art set because the coloring book only mentioned those by name.
For example:
Period 10 → alpha = 0.1818
Period 11 → alpha = 0.1667
What about wanting an alpha of 0.17, which might yield superior returns in your strategy that uses EMA? No whole-number period can provide this! Direct α parameterization offers more precision, much like how an analog tuner lets you find the perfect radio frequency while digital presets force you to choose only from predetermined stations, potentially missing the clearest signal sitting right between channels.
Sidenote: the choice of α = 1 / (1+period) is just a convention from 1970s, probably started by J. Welles Wilder, who popularized the use of the 14-day EMA. It was designed to create an approximate equivalence between EMA and SMA over the same number of periods, even thought SMA needs a period window (as it is FIR filter) and EMA doesn't. In reality, the decay factor α in EMA should be allowed any valye between 0.0 and 1.0, not just some discrete values derived from an integer-based period! Algorithmic systems should find the best α decay for EMA directly, allowing the system to fine-tune at will and not through conversion of integer period to float α decay – though this might put a few traditionalist traders into early retirement. Well, to prevent that, most traditionalist implementations of EMA only use period and no alpha at all. Heaven forbid we disturb people who print their charts on paper, draw trendlines with rulers, and insist the market "feels different" since computers do algotrading!
▶️ Calculating EMAs Efficiently
The standard textbook formula for EMA is:
EMA = CurrentPrice × alpha + PreviousEMA × (1 - alpha)
But did you know that a more efficient version exists, once you apply a tiny bit of high school algebra:
EMA = alpha × (CurrentPrice - PreviousEMA) + PreviousEMA
The first one requires three operations: 2 multiplications + 1 addition. The second one also requires three ops: 1 multiplication + 1 addition + 1 subtraction.
That's pathetic, you say? Not worth implementing? In most computational models, multiplications cost much more than additions/subtractions – much like how ordering dessert costs more than asking for a water refill at restaurants.
Relative CPU cost of float operations :
Addition/Subtraction: ~1 cycle
Multiplication: ~5 cycles (depending on precision and architecture)
Now you see the difference? 2 * 5 + 1 = 11 against 5 + 1 + 1 = 7. That is ≈ 36.36% efficiency gain just by swapping formulas around! And making your high school math teacher proud enough to finally put your test on the refrigerator.
▶️ The Warmup Problem: how to start the EMA sequence right
How do we calculate the first EMA value when there's no previous EMA available? Let's see some possible options used throughout the history:
Start with zero : EMA(0) = 0. This creates stupidly large distortion until enough bars pass for the horrible effect to diminish – like starting a trading account with zero balance but backdating a year of missed trades, then watching your balance struggle to climb out of a phantom debt for months.
Start with first price : EMA(0) = first price. This is better than starting with zero, but still causes initial distortion that will be extra-bad if the first price is an outlier – like forming your entire opinion of a stock based solely on its IPO day price, then wondering why your model is tanking for weeks afterward.
Use SMA for warmup : This is the tradition from the pencil-and-paper era of technical analysis – when calculators were luxury items and "algorithmic trading" meant your broker had neat handwriting. We first calculate an SMA over the initial period, then kickstart the EMA with this average value. It's widely used due to tradition, not merit, creating a mathematical Frankenstein that uses an FIR filter (SMA) during the initial period before abruptly switching to an IIR filter (EMA). This methodology is so aesthetically offensive (abrupt kink on the transition from SMA to EMA) that charting platforms hide these early values entirely, pretending EMA simply doesn't exist until the warmup period passes – the technical analysis equivalent of sweeping dust under the rug.
Use WMA for warmup : This one was never popular because it is harder to calculate with a pencil - compared to using simple SMA for warmup. Weighted Moving Average provides a much better approximation of a starting value as its linear descending profile is much closer to the EMA's decay profile.
These methods all share one problem: they produce inaccurate initial values that traders often hide or discard, much like how hedge funds conveniently report awesome performance "since strategy inception" only after their disastrous first quarter has been surgically removed from the track record.
▶️ A Better Way to start EMA: Decaying compensation
Think of it this way: An ideal EMA uses an infinite history of prices, but we only have data starting from a specific point. This creates a problem - our EMA starts with an incorrect assumption that all previous prices were all zero, all close, or all average – like trying to write someone's biography but only having information about their life since last Tuesday.
But there is a better way. It requires more than high school math comprehension and is more computationally intensive, but is mathematically correct and numerically stable. This approach involves compensating calculated EMA values for the "phantom data" that would have existed before our first price point.
Here's how phantom data compensation works:
We start our normal EMA calculation:
EMA_today = EMA_yesterday + α × (Price_today - EMA_yesterday)
But we add a correction factor that adjusts for the missing history:
Correction = 1 at the start
Correction = Correction × (1-α) after each calculation
We then apply this correction:
True_EMA = Raw_EMA / (1-Correction)
This correction factor starts at 1 (full compensation effect) and gets exponentially smaller with each new price bar. After enough data points, the correction becomes so small (i.e., below 0.0000000001) that we can stop applying it as it is no longer relevant.
Let's see how this works in practice:
For the first price bar:
Raw_EMA = 0
Correction = 1
True_EMA = Price (since 0 ÷ (1-1) is undefined, we use the first price)
For the second price bar:
Raw_EMA = α × (Price_2 - 0) + 0 = α × Price_2
Correction = 1 × (1-α) = (1-α)
True_EMA = α × Price_2 ÷ (1-(1-α)) = Price_2
For the third price bar:
Raw_EMA updates using the standard formula
Correction = (1-α) × (1-α) = (1-α)²
True_EMA = Raw_EMA ÷ (1-(1-α)²)
With each new price, the correction factor shrinks exponentially. After about -log₁₀(1e-10)/log₁₀(1-α) bars, the correction becomes negligible, and our EMA calculation matches what we would get if we had infinite historical data.
This approach provides accurate EMA values from the very first calculation. There's no need to use SMA for warmup or discard early values before output converges - EMA is mathematically correct from first value, ready to party without the awkward warmup phase.
Here is Pine Script 6 implementation of EMA that can take alpha parameter directly (or period if desired), returns valid values from the start, is resilient to dirty input values, uses decaying compensator instead of SMA, and uses the least amount of computational cycles possible.
// Enhanced EMA function with proper initialization and efficient calculation
ema(series float source, simple int period=0, simple float alpha=0)=>
// Input validation - one of alpha or period must be provided
if alpha<=0 and period<=0
runtime.error("Alpha or period must be provided")
// Calculate alpha from period if alpha not directly specified
float a = alpha > 0 ? alpha : 2.0 / math.max(period, 1)
// Initialize variables for EMA calculation
var float ema = na // Stores raw EMA value
var float result = na // Stores final corrected EMA
var float e = 1.0 // Decay compensation factor
var bool warmup = true // Flag for warmup phase
if not na(source)
if na(ema)
// First value case - initialize EMA to zero
// (we'll correct this immediately with the compensation)
ema := 0
result := source
else
// Standard EMA calculation (optimized formula)
ema := a * (source - ema) + ema
if warmup
// During warmup phase, apply decay compensation
e *= (1-a) // Update decay factor
float c = 1.0 / (1.0 - e) // Calculate correction multiplier
result := c * ema // Apply correction
// Stop warmup phase when correction becomes negligible
if e <= 1e-10
warmup := false
else
// After warmup, EMA operates without correction
result := ema
result // Return the properly compensated EMA value
▶️ CONCLUSION
EMA isn't just a "better SMA"—it is a fundamentally different tool, like how a submarine differs from a sailboat – both float, but the similarities end there. EMA responds to inputs differently, weighs historical data differently, and requires different initialization techniques.
By understanding these differences, traders can make more informed decisions about when and how to use EMA in trading strategies. And as EMA is embedded in so many other complex and compound indicators and strategies, if system uses tainted and inferior EMA calculatiomn, it is doing a disservice to all derivative indicators too – like building a skyscraper on a foundation of Jell-O.
The next time you add an EMA to your chart, remember: you're not just looking at a "faster moving average." You're using an INFINITE IMPULSE RESPONSE filter that carries the echo of all previous price actions, properly weighted to help make better trading decisions.
EMA done right might significantly improve the quality of all signals, strategies, and trades that rely on EMA somewhere deep in its algorithmic bowels – proving once again that math skills are indeed useful after high school, no matter what your guidance counselor told you.
Moving Averages ProxyLibrary "MovingAveragesProxy"
Moving Averages Proxy - Library of all moving averages spread out in different libraries
rvwap(_src, fixedTfInput, minsInput, hoursInput, daysInput, minBarsInput)
Calculates the Rolling VWAP (customized VWAP developed by the team of TradingView)
Parameters:
_src : (float) Source. Default: close
fixedTfInput : (bool) Use a fixed time period. Default: false
minsInput : (int) Minutes. Default: 0
hoursInput : (int) Hours. Default: 0
daysInput : (int) Days. Default: 1
minBarsInput : (int) Bars. Default: 10
Returns: (float) Rolling VWAP
correlationMa(src, len, factor)
Correlation Moving Average
Parameters:
src : (float) Source. Default: close
len : (int) Length
factor : (float) Factor. Default: 1.7
Returns: (float) Correlation Moving Average
regma(src, len, lambda)
Regularized Exponential Moving Average
Parameters:
src : (float) Source. Default: close
len : (int) Length
lambda : (float) Lambda. Default: 0.5
Returns: (float) Regularized Exponential Moving Average
repma(src, len)
Repulsion Moving Average
Parameters:
src : (float) Source. Default: close
len : (int) Length
Returns: (float) Repulsion Moving Average
epma(src, length, offset)
End Point Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
offset : (float) Offset. Default: 4
Returns: (float) End Point Moving Average
lc_lsma(src, length)
1LC-LSMA (1 line code lsma with 3 functions)
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) 1LC-LSMA Moving Average
aarma(src, length)
Adaptive Autonomous Recursive Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Adaptive Autonomous Recursive Moving Average
alsma(src, length)
Adaptive Least Squares
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Adaptive Least Squares
ahma(src, length)
Ahrens Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Ahrens Moving Average
adema(src)
Ahrens Moving Average
Parameters:
src : (float) Source. Default: close
Returns: (float) Moving Average
autol(src, lenDev)
Auto-Line
Parameters:
src : (float) Source. Default: close
lenDev : (int) Length for standard deviation
Returns: (float) Auto-Line
fibowma(src, length)
Fibonacci Weighted Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Moving Average
fisherlsma(src, length)
Fisher Least Squares Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Moving Average
leoma(src, length)
Leo Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Moving Average
linwma(src, period, weight)
Linear Weighted Moving Average
Parameters:
src : (float) Source. Default: close
period : (int) Length
weight : (int) Weight
Returns: (float) Moving Average
mcma(src, length)
McNicholl Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Moving Average
srwma(src, length)
Square Root Weighted Moving Average
Parameters:
src : (float) Source. Default: close
length : (int) Length
Returns: (float) Moving Average
EDSMA(src, len)
Ehlers Dynamic Smoothed Moving Average.
Parameters:
src : Series to use ('close' is used if no argument is supplied).
len : Lookback length to use.
Returns: EDSMA smoothing.
dema(x, t)
Double Exponential Moving Average.
Parameters:
x : Series to use ('close' is used if no argument is supplied).
t : Lookback length to use.
Returns: DEMA smoothing.
tema(src, len)
Triple Exponential Moving Average.
Parameters:
src : Series to use ('close' is used if no argument is supplied).
len : Lookback length to use.
Returns: TEMA smoothing.
smma(src, len)
Smoothed Moving Average.
Parameters:
src : Series to use ('close' is used if no argument is supplied).
len : Lookback length to use.
Returns: SMMA smoothing.
hullma(src, len)
Hull Moving Average.
Parameters:
src : Series to use ('close' is used if no argument is supplied).
len : Lookback length to use.
Returns: Hull smoothing.
frama(x, t)
Fractal Reactive Moving Average.
Parameters:
x : Series to use ('close' is used if no argument is supplied).
t : Lookback length to use.
Returns: FRAMA smoothing.
kama(x, t)
Kaufman's Adaptive Moving Average.
Parameters:
x : Series to use ('close' is used if no argument is supplied).
t : Lookback length to use.
Returns: KAMA smoothing.
vama(src, len)
Volatility Adjusted Moving Average.
Parameters:
src : Series to use ('close' is used if no argument is supplied).
len : Lookback length to use.
Returns: VAMA smoothing.
donchian(len)
Donchian Calculation.
Parameters:
len : Lookback length to use.
Returns: Average of the highest price and the lowest price for the specified look-back period.
Jurik(src, len)
Jurik Moving Average.
Parameters:
src : Series to use ('close' is used if no argument is supplied).
len : Lookback length to use.
Returns: JMA smoothing.
xema(src, len)
Optimized Exponential Moving Average.
Parameters:
src : Series to use ('close' is used if no argument is supplied).
len : Lookback length to use.
Returns: XEMA smoothing.
ehma(src, len)
EHMA - Exponential Hull Moving Average
Parameters:
src : Source
len : Period
Returns: Exponential Hull Moving Average (EHMA)
covwema(src, len)
Coefficient of Variation Weighted Exponential Moving Average (COVWEMA)
Parameters:
src : Source
len : Period
Returns: Coefficient of Variation Weighted Exponential Moving Average (COVWEMA)
covwma(src, len)
Coefficient of Variation Weighted Moving Average (COVWMA)
Parameters:
src : Source
len : Period
Returns: Coefficient of Variation Weighted Moving Average (COVWMA)
eframa(src, len, FC, SC)
Ehlrs Modified Fractal Adaptive Moving Average (EFRAMA)
Parameters:
src : Source
len : Period
FC : Lower Shift Limit for Ehlrs Modified Fractal Adaptive Moving Average
SC : Upper Shift Limit for Ehlrs Modified Fractal Adaptive Moving Average
Returns: Ehlrs Modified Fractal Adaptive Moving Average (EFRAMA)
etma(src, len)
Exponential Triangular Moving Average (ETMA)
Parameters:
src : Source
len : Period
Returns: Exponential Triangular Moving Average (ETMA)
rma(src, len)
RMA - RSI Moving average
Parameters:
src : Source
len : Period
Returns: RSI Moving average (RMA)
thma(src, len)
THMA - Triple Hull Moving Average
Parameters:
src : Source
len : Period
Returns: Triple Hull Moving Average (THMA)
vidya(src, len)
Variable Index Dynamic Average (VIDYA)
Parameters:
src : Source
len : Period
Returns: Variable Index Dynamic Average (VIDYA)
zsma(src, len)
Zero-Lag Simple Moving Average (ZSMA)
Parameters:
src : Source
len : Period
Returns: Zero-Lag Simple Moving Average (ZSMA)
zema(src, len)
Zero-Lag Exponential Moving Average (ZEMA)
Parameters:
src : Source
len : Period
Returns: Zero-Lag Exponential Moving Average (ZEMA)
evwma(src, len)
EVWMA - Elastic Volume Weighted Moving Average
Parameters:
src : Source
len : Period
Returns: Elastic Volume Weighted Moving Average (EVWMA)
tt3(src, len, a1_t3)
Tillson T3
Parameters:
src : Source
len : Period
a1_t3 : Tillson T3 Volume Factor
Returns: Tillson T3
gma(src, len)
GMA - Geometric Moving Average
Parameters:
src : Source
len : Period
Returns: Geometric Moving Average (GMA)
wwma(src, len)
WWMA - Welles Wilder Moving Average
Parameters:
src : Source
len : Period
Returns: Welles Wilder Moving Average (WWMA)
cma(src, len)
Corrective Moving average (CMA)
Parameters:
src : Source
len : Period
Returns: Corrective Moving average (CMA)
edma(src, len)
Exponentially Deviating Moving Average (MZ EDMA)
Parameters:
src : Source
len : Period
Returns: Exponentially Deviating Moving Average (MZ EDMA)
rema(src, len)
Range EMA (REMA)
Parameters:
src : Source
len : Period
Returns: Range EMA (REMA)
sw_ma(src, len)
Sine-Weighted Moving Average (SW-MA)
Parameters:
src : Source
len : Period
Returns: Sine-Weighted Moving Average (SW-MA)
mama(src, len)
MAMA - MESA Adaptive Moving Average
Parameters:
src : Source
len : Period
Returns: MESA Adaptive Moving Average (MAMA)
fama(src, len)
FAMA - Following Adaptive Moving Average
Parameters:
src : Source
len : Period
Returns: Following Adaptive Moving Average (FAMA)
hkama(src, len)
HKAMA - Hilbert based Kaufman's Adaptive Moving Average
Parameters:
src : Source
len : Period
Returns: Hilbert based Kaufman's Adaptive Moving Average (HKAMA)
getMovingAverage(type, src, len, lsmaOffset, inputAlmaOffset, inputAlmaSigma, FC, SC, a1_t3, fixedTfInput, daysInput, hoursInput, minsInput, minBarsInput, lambda, volumeWeighted, gamma_aarma, smooth, linweight, volatility_lookback, jurik_phase, jurik_power)
Abstract proxy function that invokes the calculation of a moving average according to type
Parameters:
type : (string) Type of moving average
src : (float) Source of series (close, high, low, etc.)
len : (int) Period of loopback to calculate the average
lsmaOffset : (int) Offset for Least Squares MA
inputAlmaOffset : (float) Offset for ALMA
inputAlmaSigma : (float) Sigma for ALMA
FC : (int) Lower Shift Limit for Ehlrs Modified Fractal Adaptive Moving Average
SC : (int) Upper Shift Limit for Ehlrs Modified Fractal Adaptive Moving Average
a1_t3 : (float) Tillson T3 Volume Factor
fixedTfInput : (bool) Use a fixed time period in Rolling VWAP
daysInput : (int) Days in Rolling VWAP
hoursInput : (int) Hours in Rolling VWAP
minsInput : (int) Minutrs in Rolling VWAP
minBarsInput : (int) Bars in Rolling VWAP
lambda : (float) Regularization Constant in Regularized EMA
volumeWeighted : (bool) Apply volume weighted calculation in selected moving average
gamma_aarma : (float) Gamma for Adaptive Autonomous Recursive Moving Average
smooth : (float) Smooth for Adaptive Least Squares
linweight : (float) Weight for Volume Weighted Moving Average
volatility_lookback : (int) Loopback for Volatility Adjusted Moving Average
jurik_phase : (int) Phase for Jurik Moving Average
jurik_power : (int) Power for Jurik Moving Average
Returns: (float) Moving average
Moving_AveragesLibrary "Moving_Averages"
This library contains majority important moving average functions with int series support. Which means that they can be used with variable length input. For conventional use, please use tradingview built-in ta functions for moving averages as they are more precise. I'll use functions in this library for my other scripts with dynamic length inputs.
ema(src, len)
Exponential Moving Average (EMA)
Parameters:
src : Source
len : Period
Returns: Exponential Moving Average with Series Int Support (EMA)
alma(src, len, a_offset, a_sigma)
Arnaud Legoux Moving Average (ALMA)
Parameters:
src : Source
len : Period
a_offset : Arnaud Legoux offset
a_sigma : Arnaud Legoux sigma
Returns: Arnaud Legoux Moving Average (ALMA)
covwema(src, len)
Coefficient of Variation Weighted Exponential Moving Average (COVWEMA)
Parameters:
src : Source
len : Period
Returns: Coefficient of Variation Weighted Exponential Moving Average (COVWEMA)
covwma(src, len)
Coefficient of Variation Weighted Moving Average (COVWMA)
Parameters:
src : Source
len : Period
Returns: Coefficient of Variation Weighted Moving Average (COVWMA)
dema(src, len)
DEMA - Double Exponential Moving Average
Parameters:
src : Source
len : Period
Returns: DEMA - Double Exponential Moving Average
edsma(src, len, ssfLength, ssfPoles)
EDSMA - Ehlers Deviation Scaled Moving Average
Parameters:
src : Source
len : Period
ssfLength : EDSMA - Super Smoother Filter Length
ssfPoles : EDSMA - Super Smoother Filter Poles
Returns: Ehlers Deviation Scaled Moving Average (EDSMA)
eframa(src, len, FC, SC)
Ehlrs Modified Fractal Adaptive Moving Average (EFRAMA)
Parameters:
src : Source
len : Period
FC : Lower Shift Limit for Ehlrs Modified Fractal Adaptive Moving Average
SC : Upper Shift Limit for Ehlrs Modified Fractal Adaptive Moving Average
Returns: Ehlrs Modified Fractal Adaptive Moving Average (EFRAMA)
ehma(src, len)
EHMA - Exponential Hull Moving Average
Parameters:
src : Source
len : Period
Returns: Exponential Hull Moving Average (EHMA)
etma(src, len)
Exponential Triangular Moving Average (ETMA)
Parameters:
src : Source
len : Period
Returns: Exponential Triangular Moving Average (ETMA)
frama(src, len)
Fractal Adaptive Moving Average (FRAMA)
Parameters:
src : Source
len : Period
Returns: Fractal Adaptive Moving Average (FRAMA)
hma(src, len)
HMA - Hull Moving Average
Parameters:
src : Source
len : Period
Returns: Hull Moving Average (HMA)
jma(src, len, jurik_phase, jurik_power)
Jurik Moving Average - JMA
Parameters:
src : Source
len : Period
jurik_phase : Jurik (JMA) Only - Phase
jurik_power : Jurik (JMA) Only - Power
Returns: Jurik Moving Average (JMA)
kama(src, len, k_fastLength, k_slowLength)
Kaufman's Adaptive Moving Average (KAMA)
Parameters:
src : Source
len : Period
k_fastLength : Number of periods for the fastest exponential moving average
k_slowLength : Number of periods for the slowest exponential moving average
Returns: Kaufman's Adaptive Moving Average (KAMA)
kijun(_high, _low, len, kidiv)
Kijun v2
Parameters:
_high : High value of bar
_low : Low value of bar
len : Period
kidiv : Kijun MOD Divider
Returns: Kijun v2
lsma(src, len, offset)
LSMA/LRC - Least Squares Moving Average / Linear Regression Curve
Parameters:
src : Source
len : Period
offset : Offset
Returns: Least Squares Moving Average (LSMA)/ Linear Regression Curve (LRC)
mf(src, len, beta, feedback, z)
MF - Modular Filter
Parameters:
src : Source
len : Period
beta : Modular Filter, General Filter Only - Beta
feedback : Modular Filter Only - Feedback
z : Modular Filter Only - Feedback Weighting
Returns: Modular Filter (MF)
rma(src, len)
RMA - RSI Moving average
Parameters:
src : Source
len : Period
Returns: RSI Moving average (RMA)
sma(src, len)
SMA - Simple Moving Average
Parameters:
src : Source
len : Period
Returns: Simple Moving Average (SMA)
smma(src, len)
Smoothed Moving Average (SMMA)
Parameters:
src : Source
len : Period
Returns: Smoothed Moving Average (SMMA)
stma(src, len)
Simple Triangular Moving Average (STMA)
Parameters:
src : Source
len : Period
Returns: Simple Triangular Moving Average (STMA)
tema(src, len)
TEMA - Triple Exponential Moving Average
Parameters:
src : Source
len : Period
Returns: Triple Exponential Moving Average (TEMA)
thma(src, len)
THMA - Triple Hull Moving Average
Parameters:
src : Source
len : Period
Returns: Triple Hull Moving Average (THMA)
vama(src, len, volatility_lookback)
VAMA - Volatility Adjusted Moving Average
Parameters:
src : Source
len : Period
volatility_lookback : Volatility lookback length
Returns: Volatility Adjusted Moving Average (VAMA)
vidya(src, len)
Variable Index Dynamic Average (VIDYA)
Parameters:
src : Source
len : Period
Returns: Variable Index Dynamic Average (VIDYA)
vwma(src, len)
Volume-Weighted Moving Average (VWMA)
Parameters:
src : Source
len : Period
Returns: Volume-Weighted Moving Average (VWMA)
wma(src, len)
WMA - Weighted Moving Average
Parameters:
src : Source
len : Period
Returns: Weighted Moving Average (WMA)
zema(src, len)
Zero-Lag Exponential Moving Average (ZEMA)
Parameters:
src : Source
len : Period
Returns: Zero-Lag Exponential Moving Average (ZEMA)
zsma(src, len)
Zero-Lag Simple Moving Average (ZSMA)
Parameters:
src : Source
len : Period
Returns: Zero-Lag Simple Moving Average (ZSMA)
evwma(src, len)
EVWMA - Elastic Volume Weighted Moving Average
Parameters:
src : Source
len : Period
Returns: Elastic Volume Weighted Moving Average (EVWMA)
tt3(src, len, a1_t3)
Tillson T3
Parameters:
src : Source
len : Period
a1_t3 : Tillson T3 Volume Factor
Returns: Tillson T3
gma(src, len)
GMA - Geometric Moving Average
Parameters:
src : Source
len : Period
Returns: Geometric Moving Average (GMA)
wwma(src, len)
WWMA - Welles Wilder Moving Average
Parameters:
src : Source
len : Period
Returns: Welles Wilder Moving Average (WWMA)
ama(src, _high, _low, len, ama_f_length, ama_s_length)
AMA - Adjusted Moving Average
Parameters:
src : Source
_high : High value of bar
_low : Low value of bar
len : Period
ama_f_length : Fast EMA Length
ama_s_length : Slow EMA Length
Returns: Adjusted Moving Average (AMA)
cma(src, len)
Corrective Moving average (CMA)
Parameters:
src : Source
len : Period
Returns: Corrective Moving average (CMA)
gmma(src, len)
Geometric Mean Moving Average (GMMA)
Parameters:
src : Source
len : Period
Returns: Geometric Mean Moving Average (GMMA)
ealf(src, len, LAPercLen_, FPerc_)
Ehler's Adaptive Laguerre filter (EALF)
Parameters:
src : Source
len : Period
LAPercLen_ : Median Length
FPerc_ : Median Percentage
Returns: Ehler's Adaptive Laguerre filter (EALF)
elf(src, len, LAPercLen_, FPerc_)
ELF - Ehler's Laguerre filter
Parameters:
src : Source
len : Period
LAPercLen_ : Median Length
FPerc_ : Median Percentage
Returns: Ehler's Laguerre Filter (ELF)
edma(src, len)
Exponentially Deviating Moving Average (MZ EDMA)
Parameters:
src : Source
len : Period
Returns: Exponentially Deviating Moving Average (MZ EDMA)
pnr(src, len, rank_inter_Perc_)
PNR - percentile nearest rank
Parameters:
src : Source
len : Period
rank_inter_Perc_ : Rank and Interpolation Percentage
Returns: Percentile Nearest Rank (PNR)
pli(src, len, rank_inter_Perc_)
PLI - Percentile Linear Interpolation
Parameters:
src : Source
len : Period
rank_inter_Perc_ : Rank and Interpolation Percentage
Returns: Percentile Linear Interpolation (PLI)
rema(src, len)
Range EMA (REMA)
Parameters:
src : Source
len : Period
Returns: Range EMA (REMA)
sw_ma(src, len)
Sine-Weighted Moving Average (SW-MA)
Parameters:
src : Source
len : Period
Returns: Sine-Weighted Moving Average (SW-MA)
vwap(src, len)
Volume Weighted Average Price (VWAP)
Parameters:
src : Source
len : Period
Returns: Volume Weighted Average Price (VWAP)
mama(src, len)
MAMA - MESA Adaptive Moving Average
Parameters:
src : Source
len : Period
Returns: MESA Adaptive Moving Average (MAMA)
fama(src, len)
FAMA - Following Adaptive Moving Average
Parameters:
src : Source
len : Period
Returns: Following Adaptive Moving Average (FAMA)
hkama(src, len)
HKAMA - Hilbert based Kaufman's Adaptive Moving Average
Parameters:
src : Source
len : Period
Returns: Hilbert based Kaufman's Adaptive Moving Average (HKAMA)
Demonstration of how history length affects all EMA valuesI saw some discussion of this so I whipped up an example to prove the that effect of history length on EMA values is pronounced, even for bars much further than the EMA length from the first candle of the chart.
This chart has two 89-bar EMAs of the close: a green one and a red one. However, for the red one, the first 89 bars of the graph are considered to have a close of "0", which is exactly whatTradingView's EMA calculation uses for bars before the start of the graph.
This is because unlike other moving averages, which reference the price of previous bars, the EMA references the EMA of previous bars. Therefore, bars closer to the beginning of the chart, where TradingView can't calculate an EMA because there is no previous EMA and therefore uses 0, will return substantially different values for the EMA() function that the same cart would with more history.
The further a bar is back in history, the less influence it has. However, every single historical bar has some influence on the EMA of every later bar.
To allow you to see this for yourself, this script contains the following inputs which you can change to see the effect:
-EMA period (default 89)
-Number of bars to ignore for EMA2 (default 89)
-decimal precision to show differences in. By making this a large number you can see that, although the effects diminish, history length affects all EMA values for the char.
-label spacing (increase this if you have a long history and run into TV's 50-label limit)
Multiple EMAMultiple EMA. Color switch of slowest EMA (def=200) when price close below or above. Trend marker when fastest EMA (def=9) cross slowest EMA (def=200).
Multiple EMAMultiple EMA lines. Color switch of slowest EMA (def=200) when price close above or below. Trend marker when fastest EMA (def=9) cross slowest one.
Mean Reversion Cloud (Ornstein-Uhlenbeck) // AlgoFyreThe Mean Reversion Cloud (Ornstein-Uhlenbeck) indicator detects mean-reversion opportunities by applying the Ornstein-Uhlenbeck process. It calculates a dynamic mean using an Exponential Weighted Moving Average, surrounded by volatility bands, signaling potential buy/sell points when prices deviate.
TABLE OF CONTENTS
🔶 ORIGINALITY
🔸Adaptive Mean Calculation
🔸Volatility-Based Cloud
🔸Speed of Reversion (θ)
🔶 FUNCTIONALITY
🔸Dynamic Mean and Volatility Bands
🞘 How it works
🞘 How to calculate
🞘 Code extract
🔸Visualization via Table and Plotshapes
🞘 Table Overview
🞘 Plotshapes Explanation
🞘 Code extract
🔶 INSTRUCTIONS
🔸Step-by-Step Guidelines
🞘 Setting Up the Indicator
🞘 Understanding What to Look For on the Chart
🞘 Possible Entry Signals
🞘 Possible Take Profit Strategies
🞘 Possible Stop-Loss Levels
🞘 Additional Tips
🔸Customize settings
🔶 CONCLUSION
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🔶 ORIGINALITY The Mean Reversion Cloud (Ornstein-Uhlenbeck) is a unique indicator that applies the Ornstein-Uhlenbeck stochastic process to identify mean-reverting behavior in asset prices. Unlike traditional moving average-based indicators, this model uses an Exponentially Weighted Moving Average (EWMA) to calculate the long-term mean, dynamically adjusting to recent price movements while still considering all historical data. It also incorporates volatility bands, providing a "cloud" that visually highlights overbought or oversold conditions. By calculating the speed of mean reversion (θ) through the autocorrelation of log returns, this indicator offers traders a more nuanced and mathematically robust tool for identifying mean-reversion opportunities. These innovations make it especially useful for markets that exhibit range-bound characteristics, offering timely buy and sell signals based on statistical deviations from the mean.
🔸Adaptive Mean Calculation Traditional MA indicators use fixed lengths, which can lead to lagging signals or over-sensitivity in volatile markets. The Mean Reversion Cloud uses an Exponentially Weighted Moving Average (EWMA), which adapts to price movements by dynamically adjusting its calculation, offering a more responsive mean.
🔸Volatility-Based Cloud Unlike simple moving averages that only plot a single line, the Mean Reversion Cloud surrounds the dynamic mean with volatility bands. These bands, based on standard deviations, provide traders with a visual cue of when prices are statistically likely to revert, highlighting potential reversal zones.
🔸Speed of Reversion (θ) The indicator goes beyond price averages by calculating the speed at which the price reverts to the mean (θ), using the autocorrelation of log returns. This gives traders an additional tool for estimating the likelihood and timing of mean reversion, making the signals more reliable in practice.
🔶 FUNCTIONALITY The Mean Reversion Cloud (Ornstein-Uhlenbeck) indicator is designed to detect potential mean-reversion opportunities in asset prices by applying the Ornstein-Uhlenbeck stochastic process. It calculates a dynamic mean through the Exponentially Weighted Moving Average (EWMA) and plots volatility bands based on the standard deviation of the asset's price over a specified period. These bands create a "cloud" that represents expected price fluctuations, helping traders to identify overbought or oversold conditions. By calculating the speed of reversion (θ) from the autocorrelation of log returns, the indicator offers a more refined way of assessing how quickly prices may revert to the mean. Additionally, the inclusion of volatility provides a comprehensive view of market conditions, allowing for more accurate buy and sell signals.
Let's dive into the details:
🔸Dynamic Mean and Volatility Bands The dynamic mean (μ) is calculated using the EWMA, giving more weight to recent prices but considering all historical data. This process closely resembles the Ornstein-Uhlenbeck (OU) process, which models the tendency of a stochastic variable (such as price) to revert to its mean over time. Volatility bands are plotted around the mean using standard deviation, forming the "cloud" that signals overbought or oversold conditions. The cloud adapts dynamically to price fluctuations and market volatility, making it a versatile tool for mean-reversion strategies. 🞘 How it works Step one: Calculate the dynamic mean (μ) The Ornstein-Uhlenbeck process describes how a variable, such as an asset's price, tends to revert to a long-term mean while subject to random fluctuations. In this indicator, the EWMA is used to compute the dynamic mean (μ), mimicking the mean-reverting behavior of the OU process. Use the EWMA formula to compute a weighted mean that adjusts to recent price movements. Assign exponentially decreasing weights to older data while giving more emphasis to current prices. Step two: Plot volatility bands Calculate the standard deviation of the price over a user-defined period to determine market volatility. Position the upper and lower bands around the mean by adding and subtracting a multiple of the standard deviation. 🞘 How to calculate Exponential Weighted Moving Average (EWMA)
The EWMA dynamically adjusts to recent price movements:
mu_t = lambda * mu_{t-1} + (1 - lambda) * P_t
Where mu_t is the mean at time t, lambda is the decay factor, and P_t is the price at time t. The higher the decay factor, the more weight is given to recent data.
Autocorrelation (ρ) and Standard Deviation (σ)
To measure mean reversion speed and volatility: rho = correlation(log(close), log(close ), length) Where rho is the autocorrelation of log returns over a specified period.
To calculate volatility:
sigma = stdev(close, length)
Where sigma is the standard deviation of the asset's closing price over a specified length.
Upper and Lower Bands
The upper and lower bands are calculated as follows:
upper_band = mu + (threshold * sigma)
lower_band = mu - (threshold * sigma)
Where threshold is a multiplier for the standard deviation, usually set to 2. These bands represent the range within which the price is expected to fluctuate, based on current volatility and the mean.
🞘 Code extract // Calculate Returns
returns = math.log(close / close )
// Calculate Long-Term Mean (μ) using EWMA over the entire dataset
var float ewma_mu = na // Initialize ewma_mu as 'na'
ewma_mu := na(ewma_mu ) ? close : decay_factor * ewma_mu + (1 - decay_factor) * close
mu = ewma_mu
// Calculate Autocorrelation at Lag 1
rho1 = ta.correlation(returns, returns , corr_length)
// Ensure rho1 is within valid range to avoid errors
rho1 := na(rho1) or rho1 <= 0 ? 0.0001 : rho1
// Calculate Speed of Mean Reversion (θ)
theta = -math.log(rho1)
// Calculate Volatility (σ)
sigma = ta.stdev(close, corr_length)
// Calculate Upper and Lower Bands
upper_band = mu + threshold * sigma
lower_band = mu - threshold * sigma
🔸Visualization via Table and Plotshapes
The table shows key statistics such as the current value of the dynamic mean (μ), the number of times the price has crossed the upper or lower bands, and the consecutive number of bars that the price has remained in an overbought or oversold state.
Plotshapes (diamonds) are used to signal buy and sell opportunities. A green diamond below the price suggests a buy signal when the price crosses below the lower band, and a red diamond above the price indicates a sell signal when the price crosses above the upper band.
The table and plotshapes provide a comprehensive visualization, combining both statistical and actionable information to aid decision-making.
🞘 Code extract // Reset consecutive_bars when price crosses the mean
var consecutive_bars = 0
if (close < mu and close >= mu) or (close > mu and close <= mu)
consecutive_bars := 0
else if math.abs(deviation) > 0
consecutive_bars := math.min(consecutive_bars + 1, dev_length)
transparency = math.max(0, math.min(100, 100 - (consecutive_bars * 100 / dev_length)))
🔶 INSTRUCTIONS
The Mean Reversion Cloud (Ornstein-Uhlenbeck) indicator can be set up by adding it to your TradingView chart and configuring parameters such as the decay factor, autocorrelation length, and volatility threshold to suit current market conditions. Look for price crossovers and deviations from the calculated mean for potential entry signals. Use the upper and lower bands as dynamic support/resistance levels for setting take profit and stop-loss orders. Combining this indicator with additional trend-following or momentum-based indicators can improve signal accuracy. Adjust settings for better mean-reversion detection and risk management.
🔸Step-by-Step Guidelines
🞘 Setting Up the Indicator
Adding the Indicator to the Chart:
Go to your TradingView chart.
Click on the "Indicators" button at the top.
Search for "Mean Reversion Cloud (Ornstein-Uhlenbeck)" in the indicators list.
Click on the indicator to add it to your chart.
Configuring the Indicator:
Open the indicator settings by clicking on the gear icon next to its name on the chart.
Decay Factor: Adjust the decay factor (λ) to control the responsiveness of the mean calculation. A higher value prioritizes recent data.
Autocorrelation Length: Set the autocorrelation length (θ) for calculating the speed of mean reversion. Longer lengths consider more historical data.
Threshold: Define the number of standard deviations for the upper and lower bands to determine how far price must deviate to trigger a signal.
Chart Setup:
Select the appropriate timeframe (e.g., 1-hour, daily) based on your trading strategy.
Consider using other indicators such as RSI or MACD to confirm buy and sell signals.
🞘 Understanding What to Look For on the Chart
Indicator Behavior:
Observe how the price interacts with the dynamic mean and volatility bands. The price staying within the bands suggests mean-reverting behavior, while crossing the bands signals potential entry points.
The indicator calculates overbought/oversold conditions based on deviation from the mean, highlighted by color-coded cloud areas on the chart.
Crossovers and Deviation:
Look for crossovers between the price and the mean (μ) or the bands. A bullish crossover occurs when the price crosses below the lower band, signaling a potential buying opportunity.
A bearish crossover occurs when the price crosses above the upper band, suggesting a potential sell signal.
Deviations from the mean indicate market extremes. A large deviation indicates that the price is far from the mean, suggesting a potential reversal.
Slope and Direction:
Pay attention to the slope of the mean (μ). A rising slope suggests bullish market conditions, while a declining slope signals a bearish market.
The steepness of the slope can indicate the strength of the mean-reversion trend.
🞘 Possible Entry Signals
Bullish Entry:
Crossover Entry: Enter a long position when the price crosses below the lower band with a positive deviation from the mean.
Confirmation Entry: Use additional indicators like RSI (above 50) or increasing volume to confirm the bullish signal.
Bearish Entry:
Crossover Entry: Enter a short position when the price crosses above the upper band with a negative deviation from the mean.
Confirmation Entry: Look for RSI (below 50) or decreasing volume to confirm the bearish signal.
Deviation Confirmation:
Enter trades when the deviation from the mean is significant, indicating that the price has strayed far from its expected value and is likely to revert.
🞘 Possible Take Profit Strategies
Static Take Profit Levels:
Set predefined take profit levels based on historical volatility, using the upper and lower bands as guides.
Place take profit orders near recent support/resistance levels, ensuring you're capitalizing on the mean-reversion behavior.
Trailing Stop Loss:
Use a trailing stop based on a percentage of the price deviation from the mean to lock in profits as the trend progresses.
Adjust the trailing stop dynamically along the calculated bands to protect profits as the price returns to the mean.
Deviation-Based Exits:
Exit when the deviation from the mean starts to decrease, signaling that the price is returning to its equilibrium.
🞘 Possible Stop-Loss Levels
Initial Stop Loss:
Place an initial stop loss outside the lower band (for long positions) or above the upper band (for short positions) to protect against excessive deviations.
Use a volatility-based buffer to avoid getting stopped out during normal price fluctuations.
Dynamic Stop Loss:
Move the stop loss closer to the mean as the price converges back towards equilibrium, reducing risk.
Adjust the stop loss dynamically along the bands to account for sudden market movements.
🞘 Additional Tips
Combine with Other Indicators:
Enhance your strategy by combining the Mean Reversion Cloud with momentum indicators like MACD, RSI, or Bollinger Bands to confirm market conditions.
Backtesting and Practice:
Backtest the indicator on historical data to understand how it performs in various market environments.
Practice using the indicator on a demo account before implementing it in live trading.
Market Awareness:
Keep an eye on market news and events that might cause extreme price movements. The indicator reacts to price data and might not account for news-driven events that can cause large deviations.
🔸Customize settings 🞘 Decay Factor (λ): Defines the weight assigned to recent price data in the calculation of the mean. A value closer to 1 places more emphasis on recent prices, while lower values create a smoother, more lagging mean.
🞘 Autocorrelation Length (θ): Sets the period for calculating the speed of mean reversion and volatility. Longer lengths capture more historical data, providing smoother calculations, while shorter lengths make the indicator more responsive.
🞘 Threshold (σ): Specifies the number of standard deviations used to create the upper and lower bands. Higher thresholds widen the bands, producing fewer signals, while lower thresholds tighten the bands for more frequent signals.
🞘 Max Gradient Length (γ): Determines the maximum number of consecutive bars for calculating the deviation gradient. This setting impacts the transparency of the plotted bands based on the length of deviation from the mean.
🔶 CONCLUSION
The Mean Reversion Cloud (Ornstein-Uhlenbeck) indicator offers a sophisticated approach to identifying mean-reversion opportunities by applying the Ornstein-Uhlenbeck stochastic process. This dynamic indicator calculates a responsive mean using an Exponentially Weighted Moving Average (EWMA) and plots volatility-based bands to highlight overbought and oversold conditions. By incorporating advanced statistical measures like autocorrelation and standard deviation, traders can better assess market extremes and potential reversals. The indicator’s ability to adapt to price behavior makes it a versatile tool for traders focused on both short-term price deviations and longer-term mean-reversion strategies. With its unique blend of statistical rigor and visual clarity, the Mean Reversion Cloud provides an invaluable tool for understanding and capitalizing on market inefficiencies.
GWAP (Gamma Weighted Average Price)Gamma Weighted Average Price (GWAP) Indicator
The Gamma Weighted Average Price (GWAP) is a dynamic financial indicator that applies exponentially decaying weights to historical prices to calculate a weighted average. The method leverages the exponential decay function, controlled by a gamma factor, to prioritize recent price data while gradually diminishing the influence of older observations. This approach builds upon techniques commonly found in time-series analysis, including Exponentially Weighted Moving Averages (EWMA), which are extensively used in financial modeling (Campbell, Lo & MacKinlay, 1997).
Theoretical Context and Justification
The gamma-weighted approach follows principles similar to those in Exponentially Weighted Moving Averages (EWMA), often used in volatility modeling, where weights decay exponentially over time. The exponential decay model can improve signal responsiveness compared to simple moving averages (Hyndman & Athanasopoulos, 2018). This design helps capture recent market dynamics without ignoring past trends, a common requirement in high-frequency trading systems (Bandi & Russell, 2006).
Practical Applications
1. Trend Detection:
The GWAP can help identify bullish and bearish trends:
• When the price is above GWAP, the market exhibits bullish momentum.
• Conversely, when the price is below GWAP, bearish momentum prevails.
2. Volatility Filtering:
Because of the gamma weighting mechanism, GWAP reduces the noise commonly seen in volatile markets, making it a useful tool for traders looking to smooth price fluctuations while retaining actionable signals.
3. Crossovers for Trade Signals:
Similar to moving average strategies, traders can use price crossovers with the GWAP as trade signals:
• Buy Signal: When the price crosses above the GWAP.
• Sell Signal: When the price crosses below the GWAP.
4. Adaptive Gamma Weighting:
The gamma factor allows for further customization.
• Higher gamma values (>1) place greater emphasis on older data, suitable for long-term trend analysis.
• Lower gamma values (<1) heavily weight recent price movements, ideal for fast-moving markets.
Example Use Case
A trader analyzing the S&P 500 may use a gamma factor of 0.92 with a 14-period GWAP to detect shifts in market sentiment during periods of heightened volatility. When the index price crosses above the GWAP, this could signal a potential recovery, prompting a buy entry. Conversely, when the price moves below the GWAP during a correction, it may suggest a short-selling opportunity.
Scientific References
• Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press.
• Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and Practice. OTexts.
• Bandi, F. M., & Russell, J. R. (2006). Microstructure Noise, Realized Variance, and Optimal Sampling. Econometrica.
Multiple Timeframe continuity with Crossover Alerts█ OVERVIEW
This Indicator calculates the EMA 9/20 and the RSI with its SMA on multiple timeframes and indicates their crossings. In addition this script alerts the user when crossings appear.
█ USAGE
Use the checkboxes to activate different timeframes. With the dropdown menu you can select the timeframe in minutes.
Furthermroie use the checkboxes to activate different crossovers. At the end of the settings you can find the same options for the RSI.
You can also let the script indicate only the overlapping of both indicator crossovers by using the combination option.
█ KNOWLEDGE
EMA: The ema function returns the exponentially weighted moving average. In ema weighting factors decrease exponentially. It calculates by using a formula: EMA = alpha * source + (1 - alpha) * EMA , where alpha = 2 / (length + 1).
SMA: The sma function returns the moving average, that is the sum of last y values of x, divided by y.
RSI: The RSI is classified as a momentum oscillator, measuring the velocity and magnitude of price movements. Momentum is the rate of the rise or fall in price. The RSI computes momentum as the ratio of higher closes to lower closes: stocks which have had more or stronger positive changes have a higher RSI than stocks which have had more or stronger negative changes.
RMA: Moving average used in RSI. It is the exponentially weighted moving average with alpha = 1 / length.
(Source: TradingView PineScript reference & en.wikipedia.org)
█ Credits
Thanks to @KhanPhelan with his EMA 9/20 trading idea
Credits to TradingView for their RSI function
█ Disclaimer
This is my first Script, any feedback is welcome.
