Normalized, Variety, Fast Fourier Transform Explorer [Loxx]Normalized, Variety, Fast Fourier Transform Explorer demonstrates Real, Cosine, and Sine Fast Fourier Transform algorithms. This indicator can be used as a rule of thumb but shouldn't be used in trading.
What is the Discrete Fourier Transform?
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle.
What is the Complex Fast Fourier Transform?
The complex Fast Fourier Transform algorithm transforms N real or complex numbers into another N complex numbers. The complex FFT transforms a real or complex signal x in the time domain into a complex two-sided spectrum X in the frequency domain. You must remember that zero frequency corresponds to n = 0, positive frequencies 0 < f < f_c correspond to values 1 ≤ n ≤ N/2 −1, while negative frequencies −fc < f < 0 correspond to N/2 +1 ≤ n ≤ N −1. The value n = N/2 corresponds to both f = f_c and f = −f_c. f_c is the critical or Nyquist frequency with f_c = 1/(2*T) or half the sampling frequency. The first harmonic X corresponds to the frequency 1/(N*T).
The complex FFT requires the list of values (resolution, or N) to be a power 2. If the input size if not a power of 2, then the input data will be padded with zeros to fit the size of the closest power of 2 upward.
What is Real-Fast Fourier Transform?
Has conditions similar to the complex Fast Fourier Transform value, except that the input data must be purely real. If the time series data has the basic type complex64, only the real parts of the complex numbers are used for the calculation. The imaginary parts are silently discarded.
What is the Real-Fast Fourier Transform?
In many applications, the input data for the DFT are purely real, in which case the outputs satisfy the symmetry
X(N-k)=X(k)
and efficient FFT algorithms have been designed for this situation (see e.g. Sorensen, 1987). One approach consists of taking an ordinary algorithm (e.g. Cooley–Tukey) and removing the redundant parts of the computation, saving roughly a factor of two in time and memory. Alternatively, it is possible to express an even-length real-input DFT as a complex DFT of half the length (whose real and imaginary parts are the even/odd elements of the original real data), followed by O(N) post-processing operations.
It was once believed that real-input DFTs could be more efficiently computed by means of the discrete Hartley transform (DHT), but it was subsequently argued that a specialized real-input DFT algorithm (FFT) can typically be found that requires fewer operations than the corresponding DHT algorithm (FHT) for the same number of inputs. Bruun's algorithm (above) is another method that was initially proposed to take advantage of real inputs, but it has not proved popular.
There are further FFT specializations for the cases of real data that have even/odd symmetry, in which case one can gain another factor of roughly two in time and memory and the DFT becomes the discrete cosine/sine transform(s) (DCT/DST). Instead of directly modifying an FFT algorithm for these cases, DCTs/DSTs can also be computed via FFTs of real data combined with O(N) pre- and post-processing.
What is the Discrete Cosine Transform?
A discrete cosine transform ( DCT ) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT , first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC ), digital television (such as SDTV, HDTV and VOD ), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.
The most common variant of discrete cosine transform is the type-II DCT , which is often called simply "the DCT". This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT , is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform ( DST ), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. Multidimensional DCTs ( MD DCTs) are developed to extend the concept of DCT to MD signals. There are several algorithms to compute MD DCT . A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT . One of these is the integer DCT (IntDCT), an integer approximation of the standard DCT ,: ix, xiii, 1, 141–304 used in several ISO /IEC and ITU-T international standards.
What is the Discrete Sine Transform?
In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample.
A family of transforms composed of sine and sine hyperbolic functions exists. These transforms are made based on the natural vibration of thin square plates with different boundary conditions.
The DST is related to the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions. See the DCT article for a general discussion of how the boundary conditions relate the various DCT and DST types. Generally, the DST is derived from the DCT by replacing the Neumann condition at x=0 with a Dirichlet condition. Both the DCT and the DST were described by Nasir Ahmed T. Natarajan and K.R. Rao in 1974. The type-I DST (DST-I) was later described by Anil K. Jain in 1976, and the type-II DST (DST-II) was then described by H.B. Kekra and J.K. Solanka in 1978.
Notable settings
windowper = period for calculation, restricted to powers of 2: "16", "32", "64", "128", "256", "512", "1024", "2048", this reason for this is FFT is an algorithm that computes DFT (Discrete Fourier Transform) in a fast way, generally in 𝑂(𝑁⋅log2(𝑁)) instead of 𝑂(𝑁2). To achieve this the input matrix has to be a power of 2 but many FFT algorithm can handle any size of input since the matrix can be zero-padded. For our purposes here, we stick to powers of 2 to keep this fast and neat. read more about this here: Cooley–Tukey FFT algorithm
SS = smoothing count, this smoothing happens after the first FCT regular pass. this zeros out frequencies from the previously calculated values above SS count. the lower this number, the smoother the output, it works opposite from other smoothing periods
Fmin1 = zeroes out frequencies not passing this test for min value
Fmax1 = zeroes out frequencies not passing this test for max value
barsback = moves the window backward
Inverse = whether or not you wish to invert the FFT after first pass calculation
Related indicators
Real-Fast Fourier Transform of Price Oscillator
STD-Stepped Fast Cosine Transform Moving Average
Real-Fast Fourier Transform of Price w/ Linear Regression
Variety RSI of Fast Discrete Cosine Transform
Additional reading
A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al.
Practical Fast 1-D DCT Algorithms With 11 Multiplications by Loeffler et al.
Cooley–Tukey FFT algorithm
Ahmed, Nasir (January 1991). "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing. 1 (1): 4–5. doi:10.1016/1051-2004(91)90086-Z.
DCT-History - How I Came Up With The Discrete Cosine Transform
Comparative Analysis for Discrete Sine Transform as a suitable method for noise estimation
Cerca negli script per "长江电子+半导体行业研究框架培训+pdf"
STD-Stepped Fast Cosine Transform Moving Average [Loxx]STD-Stepped Fast Cosine Transform Moving Average is an experimental moving average that uses Fast Cosine Transform to calculate a moving average. This indicator has standard deviation stepping in order to smooth the trend by weeding out low volatility movements.
What is the Discrete Cosine Transform?
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.
The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT". This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT, is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. Multidimensional DCTs (MD DCTs) are developed to extend the concept of DCT to MD signals. There are several algorithms to compute MD DCT. A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT. One of these is the integer DCT (IntDCT), an integer approximation of the standard DCT, : ix, xiii, 1, 141–304 used in several ISO/IEC and ITU-T international standards.
Notable settings
windowper = period for calculation, restricted to powers of 2: "16", "32", "64", "128", "256", "512", "1024", "2048", this reason for this is FFT is an algorithm that computes DFT (Discrete Fourier Transform) in a fast way, generally in 𝑂(𝑁⋅log2(𝑁)) instead of 𝑂(𝑁2). To achieve this the input matrix has to be a power of 2 but many FFT algorithm can handle any size of input since the matrix can be zero-padded. For our purposes here, we stick to powers of 2 to keep this fast and neat. read more about this here: Cooley–Tukey FFT algorithm
smthper = smoothing count, this smoothing happens after the first FCT regular pass. this zeros out frequencies from the previously calculated values above SS count. the lower this number, the smoother the output, it works opposite from other smoothing periods
Included
Alerts
Signals
Loxx's Expanded Source Types
Additional reading
A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al.
Practical Fast 1-D DCT Algorithms With 11 Multiplications by Loeffler et al.
Cooley–Tukey FFT algorithm
Real-Fast Fourier Transform of Price w/ Linear Regression [Loxx]Real-Fast Fourier Transform of Price w/ Linear Regression is a indicator that implements a Real-Fast Fourier Transform on Price and modifies the output by a measure of Linear Regression. The solid line is the Linear Regression Trend of the windowed data, The green/red line is the Real FFT of price.
What is the Discrete Fourier Transform?
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle.
What is the Complex Fast Fourier Transform?
The complex Fast Fourier Transform algorithm transforms N real or complex numbers into another N complex numbers. The complex FFT transforms a real or complex signal x in the time domain into a complex two-sided spectrum X in the frequency domain. You must remember that zero frequency corresponds to n = 0, positive frequencies 0 < f < f_c correspond to values 1 ≤ n ≤ N/2 −1, while negative frequencies −fc < f < 0 correspond to N/2 +1 ≤ n ≤ N −1. The value n = N/2 corresponds to both f = f_c and f = −f_c. f_c is the critical or Nyquist frequency with f_c = 1/(2*T) or half the sampling frequency. The first harmonic X corresponds to the frequency 1/(N*T).
The complex FFT requires the list of values (resolution, or N) to be a power 2. If the input size if not a power of 2, then the input data will be padded with zeros to fit the size of the closest power of 2 upward.
What is Real-Fast Fourier Transform?
Has conditions similar to the complex Fast Fourier Transform value, except that the input data must be purely real. If the time series data has the basic type complex64, only the real parts of the complex numbers are used for the calculation. The imaginary parts are silently discarded.
Inputs:
src = source price
uselreg = whether you wish to modify output with linear regression calculation
Windowin = windowing period, restricted to powers of 2: "4", "8", "16", "32", "64", "128", "256", "512", "1024", "2048"
Treshold = to modified power output to fine tune signal
dtrendper = adjust regression calculation
barsback = move window backward from bar 0
mutebars = mute bar coloring for the range
Further reading:
Real-valued Fast Fourier Transform Algorithms IEEE Transactions on Acoustics, Speech, and Signal Processing, June 1987
Related indicators utilizing Fourier Transform
Fourier Extrapolator of Variety RSI w/ Bollinger Bands
Fourier Extrapolation of Variety Moving Averages
Fourier Extrapolator of Price w/ Projection Forecast
PDFMA Awesome Oscillator [Loxx]Theory:
Bill Williams's Awesome Oscillator Technical Indicator (AO) is a 34-period simple moving average, plotted through the bars midpoints (H+L)/2, which is subtracted from the 5-period simple moving average, built across the bars midpoints (H+L)/2. It shows us quite clearly what’s happening to the market driving force at the present moment.
This version uses PdfMA (Probability Density Function weighted Moving Average) instead of SMA (Simple Moving Average). This is a deviation from the original AO since in the AO since there is no parameter that you can change, but with this version, you can change the variance part of the PdfMA calculation. That way you can get different values for the AO even without changing periods of calculation (the general rule of thumb is: the greater the variance, the smoother the result)
Usage:
You can use color changes (mainly on zero cross) for trend change signals
Probability Density Function based MA MACD [Loxx]Probability Density Function based MA MACD is a MACD indicator using a type of weighted moving average.
What is Probability Density Function based MA MACD?
Probability density function based MA is a sort of weighted moving average that uses probability density function to calculate the weights.
Included:
-Toggle on/off bar coloring
Haydens RSI CompanionPreface: I'm just the bartender serving today's freshly blended concoction; I'd like to send a massive THANK YOU to all the coders and PineWizards for the locally-sourced ingredients. I am simply a code editor, not a code author. The book that inspired this indicator is a free download, plus all of the pieces I used were free code from the community; my hope is that any additional useful development of The Complete RSI is also offered open-source to the community for collaboration.
Features: Fibonacci retracement plus targets. Advanced dual data ticker. Heiken Ashi or bar overlay. Hayden, BarefootJoey, Tradingview, or Custom watermark of choice. Trend lines for spotting wedges, triangles, pennants, etc. Divergences for spotting potential reversals and Momentum Discrepancy Reversal Point opportunities. Percent change and price pivot labels with advanced data & retracement targets upon hover.
‼ IMPORTANT: Hover over labels for advanced information, like targets. Google & read John Hayden's "The Complete RSI" pdf book for comprehensive instructions before attempting to trade with this indicator. Always keep an eye on higher/stronger timeframes. See the companion oscillator here:
⚠ DISCLAIMER: DYOR. Not financial advice. Not a trading system. I am not affiliated with TradingView or John Hayden; this is my own personally PineScripted presentation of a suitable RSI chart companion to use when trading according to Hayden's rules.
About the Editor: I am a former-FINRA Registered Representative, inventor/patent-holder, and self-taught PineScripter. I mostly code on a v3 Pinescript level so expect heavy scripts that could use some shortening with modern conventions.
Hayden's Advanced Relative Strength Index (RSI)Preface: I'm just the bartender serving today's freshly blended concoction; I'd like to send a massive THANK YOU to @iFuSiiOnzZ, @Koalafied_3, @LonesomeTheBlue, @LazyBear, @dgtrd and the rest of the PineWizards for the locally-sourced ingredients. I am simply a code editor, not a code author. The book that inspired this indicator is a free download, plus all of the pieces I used were free code from the PineWizards; my hope is that any additional useful development of The Complete RSI trading system also is offered open-source to the community for collaboration.
Features: Fixed & Custom price targeting. Triple trend state detection. Advanced data ticker. Candles, bars, or line RSI . Stochastic of over 20 indicators for adjustable entry/exit signals. Customizable trader watermark. Trend lines for spotting wedges , triangles, pennants , etc. Divergences for spotting potential reversals and Momentum Discrepancy Reversal Point opportunities. RSI percent change and price pivot labels. Gradient bar coloring on-chart.
‼ IMPORTANT: Hover over labels for additional information. Google & read John Hayden's "The Complete RSI" pdf book for comprehensive instructions before attempting to trade with this indicator. Always keep an eye on higher/stronger timeframes.
⚠ DISCLAIMER: DYOR. Not financial advice. Not a trading system. I am not affiliated with TradingView or John Hayden; this is my own personally PineScripted presentation of a suitable RSI to use when trading according to Hayden's rules.
About the Editor: I am a former-FINRA Registered Representative, inventor/patent-holder, and self-taught PineScripter. I mostly code on a v3 Pinescript level so expect heavy scripts that could use some shortening with modern conventions.
Hayden's RSI Rules:
📈 An Uptrend is indicated when:
1. RSI is in the 80 to 40 range
2. The chart shows simple bearish divergence
3. The chart shows Hidden bullish divergence
4. The chart shows Momentum Discrepancy Reversal Up
5. Upside targets being hit
6. 9-bar simple MA is greater than the 45-bar EMA on RSI
7. Counter-trend declines do not exceed 50% of the previous rally
🔮 An Uptrend is in danger when:
1. Longer timeframe fading rally
2. a) Multiple long-term bearish divergences. b) Upside targets not being hit.
3. 9-bar simple MA is less than the 45-bar EMA on RSI
4. Hidden bearish divergence, or simple bullish divergence
5. Deep counter-trend retracements greater than 50%
📉 A Downtrend is indicated when:
1. RSI is in the 60 to 20 range
2. The chart shows simple bullish divergences.
3. The chart shows Hidden bearish divergence
4. The chart shows Momentum Discrepancy Reversal Down
5. Downside targets being hit
6. 9-bar simple MA is less than the 45-bar EMA on RSI
7. Counter-trend rallies do not exceed 50% of the previous decline
🔮 A Downtrend is in danger when:
1. Longer timeframe fading decline
2. a) Multiple long-term bullish divergences. b) Downside targets not being hit.
3. 9-bar simple MA is greater than the 45-bar EMA on RSI
4. Hidden bullish divergence , or simple bearish divergence
5. Steep counter-trend retracements greater than 50%
MathProbabilityDistributionLibrary "MathProbabilityDistribution"
Probability Distribution Functions.
name(idx) Indexed names helper function.
Parameters:
idx : int, position in the range (0, 6).
Returns: string, distribution name.
usage:
.name(1)
Notes:
(0) => 'StdNormal'
(1) => 'Normal'
(2) => 'Skew Normal'
(3) => 'Student T'
(4) => 'Skew Student T'
(5) => 'GED'
(6) => 'Skew GED'
zscore(position, mean, deviation) Z-score helper function for x calculation.
Parameters:
position : float, position.
mean : float, mean.
deviation : float, standard deviation.
Returns: float, z-score.
usage:
.zscore(1.5, 2.0, 1.0)
std_normal(position) Standard Normal Distribution.
Parameters:
position : float, position.
Returns: float, probability density.
usage:
.std_normal(0.6)
normal(position, mean, scale) Normal Distribution.
Parameters:
position : float, position in the distribution.
mean : float, mean of the distribution, default=0.0 for standard distribution.
scale : float, scale of the distribution, default=1.0 for standard distribution.
Returns: float, probability density.
usage:
.normal(0.6)
skew_normal(position, skew, mean, scale) Skew Normal Distribution.
Parameters:
position : float, position in the distribution.
skew : float, skewness of the distribution.
mean : float, mean of the distribution, default=0.0 for standard distribution.
scale : float, scale of the distribution, default=1.0 for standard distribution.
Returns: float, probability density.
usage:
.skew_normal(0.8, -2.0)
ged(position, shape, mean, scale) Generalized Error Distribution.
Parameters:
position : float, position.
shape : float, shape.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.ged(0.8, -2.0)
skew_ged(position, shape, skew, mean, scale) Skew Generalized Error Distribution.
Parameters:
position : float, position.
shape : float, shape.
skew : float, skew.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.skew_ged(0.8, 2.0, 1.0)
student_t(position, shape, mean, scale) Student-T Distribution.
Parameters:
position : float, position.
shape : float, shape.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.student_t(0.8, 2.0, 1.0)
skew_student_t(position, shape, skew, mean, scale) Skew Student-T Distribution.
Parameters:
position : float, position.
shape : float, shape.
skew : float, skew.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.skew_student_t(0.8, 2.0, 1.0)
select(distribution, position, mean, scale, shape, skew, log) Conditional Distribution.
Parameters:
distribution : string, distribution name.
position : float, position.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
shape : float, shape.
skew : float, skew.
log : bool, if true apply log() to the result.
Returns: float, probability.
usage:
.select('StdNormal', __CYCLE4F__, log=true)
Mobility Oscillator [CC]The Mobility Oscillator was created by Mel Widner (Stocks and Commodities Feb 1996) and this is another of my ongoing series of undiscovered gems. I would say this is probably the most complicated script I have written for an indicator. It is extremely complicated to calculate comparing to other indicators but this is essentially an overbought and oversold indicator that uses a very unique technique to calculate overbought and oversold levels and overall upward or downward momentum there is in the underlying stock. It uses a price distribution function to determine how often the current prices fall within the current trend which tells us how strong the momentum for the current trend actually is. I had to customize this indicator a bit to give clear buy and sell readings so I had to introduce a lag in exchange for clearer signals. This indicator ranges between +100 and -100 and when it stays at the +100 level for example then this means a sustained uptrend and vice versa. I have included strong buy and sell signals in addition to normal ones so strong signals are darker in color and normal signals are lighter in color. Buy when the line turns green and sell when it turns red.
Let me know if there are any other scripts or indicators you would like to see me publish!
Probability Distribution HistogramProbability Distribution Histogram
During data exploration it is often useful to plot the distribution of the data one is exploring. This indicator plots the distribution of data between different bins.
Essentially, what we do is we look at the min and max of the entire data set to determine its range. When we have the range of the data, we decide how many bins we want to divide this range into, so that the more bins we get, the smaller the range (a.k.a. width) for each bin becomes. We then place each data point in its corresponding bin, to see how many of the data points end up in each bin. For instance, if we have a data set where the smallest number is 5 and the biggest number is 105, we get a range of 100. If we then decide on 20 bins, each bin will have a width of 5. So the left-most bin would therefore correspond to values between 5 and 10, and the bin to the right would correspond to values between 10 and 15, and so on.
Once we have distributed all the data points into their corresponding bins, we compare the count in each bin to the total number of data points, to get a percentage of the total for each bin. So if we have 100 data points, and the left-most bin has 2 data points in it, that would equal 2%. This is also known as probability mass (or well, an approximation of it at least, since we're dealing with a bin, and not an exact number).
Usage
This is not an indicator that will give you any trading signals. This indicator is made to help you examine data. It can take any input you give it and plot how that data is distributed.
The indicator can transform the data in a few ways to help you get the most out of your data exploration. For instance, it is usually more accurate to use logarithmic data than raw data, so there is an option to transform the data using the natural logarithmic function. There is also an option to transform the data into %-Change form or by using data differencing.
Another option that the indicator has is the ability to trim data from the data set before plotting the distribution. This can help if you know there are outliers that are made up of corrupted data or data that is not relevant to your research.
I also included the option to plot the normal distribution as well, for comparison. This can be useful when the data is made up of residuals from a prediction model, to see if the residuals seem to be normally distributed or not.
TDI - Traders Dynamic Index + RSI Divergences + Buy/Sell SignalsTraders Dynamic Index + RSI Divergences + Buy/Sell Signals
Credits to LazyBear (original code author) and JustUncleL (modifications)..
I added some new features:
1- RSI Divergences (Original code from 'Divergence Indicator')
2- Buy/Sell Signals with alerts (Green label 'Buy' - Red label 'Sell')
3- Background colouring when RSI (Green line) crosses above MBL (yellow line)
- Buy and Sell Signals are generated using Dean Malone's method (The Author of the TDI indicator) as mentioned in his PDF: (( www.forexfactory.com )), according to:
** Buy (Green Label) = RSI > 50, Red line, & Yellow line
** Sell (Red Label) = RSI < 50, Red line, & Yellow line
- I found that the best quality long trades generated when RSI crosses above red line, yellow line and they are all above 50, and vice versa for sell trades.
-I figured out another way to generate Buy/Sell Signals when RSI crosses above the yellow line, and you can stay with the trade till RSI crosses under the yellow line (I made a background colouring for that to be easily detected)
Hope you all wonderful trades..
مؤلف المؤشر هو (Dean Malone)
وكتب LazyBear كوده في tradingview
وأضاف JustUncleL بعض التعديلات عليه
أضفت إليه بعض المزايا الأخرى المتمثلة في:
1- رصد انحرافات مؤشر القوة النسبية
2- إشارات بيع وشراء بناء على طريقة مؤلف المؤشر
3- تظليل بالأخضر للمنطقة التي يعبر فيها مؤشر القوة النسبية الخط الأوسط (الخط الأصفر)
إشارات البيع والشراء تكون كالتالي:
** الشراء عندما يكون مؤشر القوة النسبية فوق الخط الأحمر وفوق خط الـ 50 وفوق الخط الأصفر
** البيع عندما يكون مؤشر القوة النسبية تحت الخط الأحمر وتحت خط الـ 50 وتحت الخط الأصفر
** أفضل إشارات الشراء حينما يعبر مؤشر القوة النسبية فوق الخط الأحمر والأصفر، ويكونوا جميعا فوق خط الـ 50، والعكس بالنسبة لإشارات البيع
يمكن استخدام المؤشر في دخول صفقات متوسط المدى، وذلك عندما يعبر مؤشر القوة النسبية فوق الخط الأصفر (قمت بتظليل المنطقة بالأخضر لسهولة رصدها) والخروج من الصفقة إذا نزل مؤشر القوة النسبية عن الخط الأصفر،
يرجى التنبه إلى أن الدخول والخروج يكون بأسباب فنية مدروسة، والمؤشر يدعم قراراتك فقط، ولا يمكن الاعتماد عليه منفردا في تحديد نقاط الدخول أوالخروج.
تجارة موفقة لكم جميعا :)
A Useful MA Weighting Function For Controlling Lag & SmoothnessSo far the most widely used moving average with an adjustable weighting function is the Arnaud Legoux moving average (ALMA), who uses a Gaussian function as weighting function. Adjustable weighting functions are useful since they allow us to control characteristics of the moving average such as lag and smoothness.
The following moving average has a simple adjustable weighting function that allows the user to have control over the lag and smoothness of the moving average, we will see that it can also be used to get both an SMA and WMA.
A high-resolution gradient is also used to color the moving average, makes it fun to watch, the plot transition between 200 colors, would be tedious to make but everything was made possible using a custom R script, I only needed to copy and paste the R console output in the Pine editor.
Settings
length : Period of the moving average
-Lag : Setting decreasing the lag of the moving average
+Lag : Setting increasing the lag of the moving average
Estimating Existing Moving Averages
The weighting function of this moving average is derived from the calculation of the beta distribution, advantages of such distribution is that unlike a lot of PDF, the beta distribution is defined within a specific range of values (0,1). Parameters alpha and beta controls the shape of the distribution, with alpha introducing negative skewness and beta introducing positive skewness, while higher values of alpha and beta increase kurtosis.
Here -Lag is directly associated to beta while +Lag is associated with alpha . When alpha = beta = 1 the distribution is uniform, and as such can be used to compute a simple moving average.
Moving average with -Lag = +Lag = 1 , its impulse response is shown below.
It is also possible to get a WMA by increasing -Lag , thus having -Lag = 2 and +Lag = 1 .
Using values of -Lag and +Lag equal to each other allows us to get a symmetrical impulse response, increasing these two values controls the heaviness of the tails of the impulse response.
Here -Lag = +Lag = 3 , note that when the impulse response of a moving average is symmetrical its lag is equal to (length-1)/2 .
As for the gradient, the color is determined by the value of an RSI using the moving average as input.
I don't promise anything but I will try to respond to your comments
[blackcat] L2 Ehlers Fisher Transform of N-bar Price ChannelLevel: 2
Background
John F. Ehlers introuced Fisher Transform of Normalize Price to a N-Day Channel in his "Cybernetic Analysis for Stocks and Futures" chapter 1 on 2004.
Function
The Fisher transform changes the PDF of any waveform so that the transformed output has an approximately Gaussian PDF. So what does this mean for trading? If the prices are normalized to fall within the range from −1 to +1 and subjected to the Fisher transform, extreme price movements are relatively rare events. This means the turning points can be clearly and unambiguously identified.
Key Signal
Fish ---> Fisher transform fast line
Fish ---> Fisher transform slow line
Pros and Cons
100% John F. Ehlers definition translation of original work, even variable names are the same. This help readers who would like to use pine to read his book. If you had read his works, then you will be quite familiar with my code style.
Remarks
The 21th script for Blackcat1402 John F. Ehlers Week publication.
Readme
In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts.
The scripts posted are categorized into 5 levels according to my efforts or manhours put into these works.
Level 1 : interesting script snippets or distinctive improvement from classic indicators or strategy. Level 1 scripts can usually appear in more complex indicators as a function module or element.
Level 2 : composite indicator/strategy. By selecting or combining several independent or dependent functions or sub indicators in proper way, the composite script exhibits a resonance phenomenon which can filter out noise or fake trading signal to enhance trading confidence level.
Level 3 : comprehensive indicator/strategy. They are simple trading systems based on my strategies. They are commonly containing several or all of entry signal, close signal, stop loss, take profit, re-entry, risk management, and position sizing techniques. Even some interesting fundamental and mass psychological aspects are incorporated.
Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop.
Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.
Volatility GuppyBased on my previous script "Turtle N Normalized," this script plots the CM SuperGuppy on the value of N to identify changing trends in the volatility of any instrument.
Turtle rules taken from an online PDF:
"The Turtles used a concept that Richard Dennis and Bill Eckhardt called N to represent the underlying volatility of a particular market.
N is simply the 20-day exponential moving average of the True Range, which is now more commonly known as the ATR. Conceptually, N represents the average range in price movement that a particular market makes in a single day, accounting for opening gaps. N was measured in the same points as the underlying contract.
The Turtles built positions in pieces which we called Units. Units were sized so that 1 N represented 1% of the account equity. Thus, a unit for a given market or commodity can be calculated using the following formula:
Unit = 1% of Account/(N x Dollars per Point)"
To normalize the Unit formula, this script instead takes the value of (close/N). Dollars per point = 1 for stocks and crypto, but will change depending on the contract specifications for individual futures .
"Since the Turtles used the Unit as the base measure for position size, and since those units were volatility risk adjusted, the Unit was a measure of both the risk of a position, and of the entire portfolio of positions."
When the EMA's are green, volatility is decreasing.
When the EMA's are red, volatility is increasing.
When the EMA's are grey, the trend is changing.
Turtle N NormalizedSimple script that calculates the normalized value of N. Rules taken from an online PDF containing the original Turtle system:
"The Turtles used a volatility-based constant percentage risk position sizing algorithm. The Turtles used a concept that Richard Dennis and Bill Eckhardt called N to represent the underlying volatility of a particular market.
N is simply the 20-day exponential moving average of the True Range, which is now more commonly known as the ATR. Conceptually, N represents the average range in price movement that a particular market makes in a single day, accounting for opening gaps. N was measured in the same points as the underlying contract.
The Turtles built positions in pieces which we called Units. Units were sized so that 1 N represented 1% of the account equity. Thus, a unit for a given market or commodity can be calculated using the following formula:
Unit = 1% of Account/(N x Dollars per Point)"
To normalize the Unit formula, this script instead takes the value of (close/N). Dollars per point = 1 for stocks and crypto, but will change depending on the contract specifications for individual futures.
"Since the Turtles used the Unit as the base measure for position size, and since those units were volatility risk adjusted, the Unit was a measure of both the risk of a position, and of the entire portfolio of positions."
When the value of N is high, volatility is low and you should be more risk-on.
When the value of N is low, volatility is high and you should be more risk-off.
Combo Backtest 123 Reversal & Fisher Transform Indicator This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
Market prices do not have a Gaussian probability density function
as many traders think. Their probability curve is not bell-shaped.
But trader can create a nearly Gaussian PDF for prices by normalizing
them or creating a normalized indicator such as the relative strength
index and applying the Fisher transform. Such a transformed output
creates the peak swings as relatively rare events.
Fisher transform formula is: y = 0.5 * ln ((1+x)/(1-x))
The sharp turning points of these peak swings clearly and unambiguously
identify price reversals in a timely manner.
WARNING:
- For purpose educate only
- This script to change bars colors.
Combo Strategy 123 Reversal & Fisher Transform Indicator This is combo strategies for get a cumulative signal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
Market prices do not have a Gaussian probability density function
as many traders think. Their probability curve is not bell-shaped.
But trader can create a nearly Gaussian PDF for prices by normalizing
them or creating a normalized indicator such as the relative strength
index and applying the Fisher transform. Such a transformed output
creates the peak swings as relatively rare events.
Fisher transform formula is: y = 0.5 * ln ((1+x)/(1-x))
The sharp turning points of these peak swings clearly and unambiguously
identify price reversals in a timely manner.
WARNING:
- For purpose educate only
- This script to change bars colors.
Noro's RiskTurtle StrategyThe idea of this strategy script was taken here:
(PDF-Book, English) bigpicture.typepad.com
Strategy
2 Donchian price channels are being created. Fast and slow. The number of candles for the channels is selected by the user. By default, 20 bars for fast and 50 bars for slow. Blue lines show a slow price channel . And used to enter positions. Using market stop orders. A fast price channel is needed to find out the price for stop-loss. This is the center line of the fast channel. Shown by a red line. The background shows when the positions were opened. Lime background for long positions, and red background for short positions. There is no background if there are no positions.
Risk size
Stop Placement
The Turtles placed their stops based on position risk. No trade could incur more than 2% risk.
Since 1N of price movement represented 1% of Account Equity, the maximum stop
that would allow 2% risk would be 2N of price movement. Turtle stops were set at 2N
below the entry for long positions, and 2N above the entry for short positions.
For
- XBT/USD, BTC /USD, BTC /USDT, ETH/USD, ETH/USDT, etc - need ***/(T)USD(T)
- Timeframes 1h, 2h, 3h, 4h
Weis pip zigzag jayyWhat you see here is the Weis pip zigzag wave plotted directly on the price chart. This script is the companion to the Weis pip wave ( ) which is plotted in the lower panel of the displayed chart and can be used as an alternate way of plotting the same results. The Weis pip zigzag wave shows how far in terms of price a Weis wave has traveled through the duration of a Weis wave. The Weis pip zigzag wave is used in combination with the Weis cumulative volume wave. The two waves must be set to the same "wave size".
To use this script you must set the wave size. Using the traditional Weis method simply enter the desired wave size in the box "Select Weis Wave Size" In this example, it is set to 5. Each wave for each security and each timeframe requires its own wave size. Although not the traditional method a more automatic way to set wave size would be to use ATR. This is not the true Weis method but it does give you similar waves and, importantly, without the hassle described above. Once the Weis wave size is set then the pip wave will be shown.
I have put a pip zigzag of a 5 point Weis wave on the bar chart - that is a different script. I have added it to allow your eye to see what a Weis wave looks like. You will notice that the wave is not in straight lines connecting wave tops to bottoms this is a function of the limitations of Pinescript version 1. This script would need to be in version 4 to allow straight lines. There are too many calculations within this script to allow conversion to Pinescript version 4 or even Version 3. I am in the process of rewriting this script to reduce the number of calculations and streamline the algorithm.
The numbers plotted on the chart are calculated to be relative numbers. The script is limited to showing only three numbers vertically. Only the highest three values of a number are shown. For example, if the highest recent pip value is 12,345 only the first 3 numerals would be displayed ie 123. But suppose there is a recent value of 691. It would not be helpful to display 691 if the other wave size is shown as 123. To give the appropriate relative value the script will show a value of 7 instead of 691. This informs you of the relative magnitude of the values. This is done automatically within the script. There is likely no need to manually override the automatically calculated value. I will create a video that demonstrates the manual override method.
What is a Weis wave? David Weis has been recognized as a Wyckoff method analyst he has written two books one of which, Trades About to Happen, describes the evolution of the now popular Weis wave. The method employed by Weis is to identify waves of price action and to compare the strength of the waves on characteristics of wave strength. Chief among the characteristics of strength is the cumulative volume of the wave. There are other markers that Weis uses as well for example how the actual price difference between the start of the Weis wave from start to finish. Weis also uses time, particularly when using a Renko chart. Weis specifically uses candle or bar closes to define all wave action ie a line chart.
David Weis did a futures io video which is a popular source of information about his method.
This is the identical script with the identical settings but without the offending links. If you want to see the pip Weis method in practice then search Weis pip wave. If you want to see Weis chart in pdf then message me and I will give a link or the Weis pdf. Why would you want to see the Weis chart for May 27, 2020? Merely to confirm the veracity of my algorithm. You could compare my Weis chart here () from the same period to the David Weis chart from May 27. Both waves are for the ES!1 4 hour chart and both for a wave size of 5.
Weis Pip Wave jayyWhat you see here is the Weis pip wave. The Weis pip wave shows how far in price a Weis wave has traveled through the duration of a Weis wave. The Weis pip wave is used in combination with the Weis cumulative volume wave. The two waves must be set to the same "wave size" and using the same method as described by Weis.
Using the traditional Weis method simply enter the desired wave size in the box "Select Weis Wave Size". In the example shown, it is set to 5 points. Each wave for each security and each timeframe requires its own wave size. Although not the traditional method a more automatic way to set wave size would be to use ATR. This is not the true Weis method but it does give you similar waves and, importantly, without the hassle of selecting a wave size for every chart. Once the Weis wave size is set then the pip wave will be shown.
I have put a zigzag of a 5 point Weis wave on the above bar chart. I have added it to allow your eye to get a better appreciation for Weis wave pivot points. You will notice that the wave is not in straight lines connecting wave tops to bottoms this is a function of the limitations of Pinescript version 1. This script would need to be in version 4 to allow straight lines. I will elaborate on the Weis pip zigzag script.
What is a Weis wave? David Weis has been recognized as a Wyckoff method analyst he has written two books one of which, Trades About to Happen, describes the evolution of the now popular Weis wave. The method employed by Weis is to identify waves of price action and to compare the strength of the waves on characteristics of wave strength. Chief among the characteristics of strength is the cumulative volume of the wave. There are other markers that Weis uses as well for example how the actual price difference between the start of the Weis wave from start to finish. Weis also uses time, particularly when using a Renko chart. Weis specifically uses candle/bar closes to define all wave action.
David Weis did a futures.io video which is a popular source of information about his method.
Cheers jayy
PS This script was published a day ago, however, I had included some links to the website of a person that uses Weis pip waves and also a dropbox link that contains the Weis wave chart for May 27, 2020, published by David Weis. Providing those links is against TV policy and so the script was hidden by TV. This is the identical script with the identical settings but without the offending links. If you want to see the pip Weis method in practice then search Weis pip wave. I have absolutely no affiliation. If you want to see Weis chart in pdf then message me and I will give a link or the Weis pdf. Why would you want to see the Weis chart for May 27, 2020? Merely to confirm the veracity of my algorithm. You could compare my chart () from the same period to the Weis chart. Both waves are for the ES!1 4 hour chart and both for a wave size of 5.
Instantaneous Trendline Strategy [ChuckBanger]Based on Instantaneous Trendline, by John Ehlers , identifies the market trend by doing removing cycle component. I think, this simplicity is what makes it attractive :) To understand Ehlers's thought process behind this, refer to the PDF linked below.
There are atleast 6 variations of this ITrend. This version is from his early presentations. You can find it here: www.mesasoftware.com
This is better then a regular MA cross over strategy
MACD Leader [ChuckBanger]MACD makes use of moving averages and therefor usually lags behind the price. It is possible to eliminate lag completely but the work around of this is usually by adding a component of the price/MA difference back to MA. This technique is called Zero-lag. It is not zero lag but it is close enough. "MACD Leader" makes use of this to form a leading signal to MACD.
First proposed by Giorgos E. Siligardos, "Leader" leads normal MACD , especially when significant trend changes are about to take place. This has the following features:
- It is similar to MACD in smoothness.
- It can be plotted along with MACD in the same window using the same scaling.
- It has the ability to lead MACD at critical situations
For detailed discussion on the various divergence patterns, refer to the PDF here: drive.google.com
This script provide an option to plot MACD and MACD leader signal on the same pane. You can enable/disable them how you want via options page. It also has the option to change to different MA types.
Wave Period Oscillator by KIVANC fr3762WPO – Wave Period Oscillator
A Time Cycle Oscillator – Published on IFTA Journal 2018 by Akram El Sherbini (pages 68-77)
(http:www.ftaa.org.hk/Files/2018130101754DGQ1JB2OUG. pdf )
Bullish signals are generated when WPO crosses over 0
Bearish signals are generated when WPO crosses under 0
OverBought level is 2
OverSold level is -2
ExtremeOB level is 2.7
ExtremeOS level is -2.7
As with most oscillators, divergences can be taken advantage of.
via PROREALCODE
Here's the link to a complete list of all my indicators:
tr.tradingview.com
Şimdiye kadar Tradingview'a eklediğim tüm indikatörlerin tam listesi için:
tr.tradingview.com
