Correlation for Major Markets This indicator plots the correlation of major markets as an indicator. The major markets covered are the following:
DXY
GC
CL
ES
RTY
ZN
The chart shows all the correlations and cross-correlations of the above instruments plotted together. The user can go in the settings and choose what correlation to see, or if multiple correlations, choose to plot the indicator a second time.
Correlation
Linear Correlation Coefficient W/ MAs and Significance TestsThis Linear CC takes into account the log-normal distribution of stock prices and performs Pearson correlation on that data set. It also smoothens the results into an easy to read oscillator, and performs a two-tail t-test on the correlation coefficient data (with a = 0.05) to determine the significance of the coefficients. Significant results are shown in a solid yellow color while insignificant results are shown in a dark yellow color (you can eyeball this with a normal LCC by looking at results around -0.5 to +0.5).
Two MAs are provided as well for a quick trend analysis. You can reduce the lookback period, but it defaults to 31 for the sake of statistical standards.
Correlation TrackerCorrelation Tracker Indicator
The Correlation Tracker indicator calculates and visualizes the correlation between two symbols on a chart. It helps traders and investors understand the relationship and strength of correlation between the selected symbol and another symbol of their choice.
Indicator Features:
- Correlation Calculation: The indicator calculates the correlation between two symbols based on the provided lookback period.
- Correlation Scale: The correlation value is normalized to a scale ranging from 0 to 1 for easy interpretation.
- Table Display: A table is displayed on the chart showing the correlation value and a descriptive label indicating the strength of the correlation.
- Customization Options: Users can customize the text color, table background color, and choose whether to display the Pearson correlation value.
- The Correlation Tracker indicator utilizes a logarithmic scale calculation, making it particularly suitable for longer timeframes such as weekly charts, thereby providing a more accurate and balanced measure of correlations across a wide range of values.
How to Use:
1. Select the symbol for which you want to track the correlation (default symbol is "SPX").
2. Adjust the lookback period to define the historical data range for correlation calculation.
3. Customize the text color and table background color according to your preference.
4. Choose whether to display the Pearson correlation value or a descriptive label for correlation strength.
5. Observe the correlation line on the chart, which changes color based on the strength of the correlation.
6. Refer to the correlation table for the exact correlation value or the descriptive label indicating the correlation strength.
Note: The indicator can be applied to any time frame chart and is not limited to logarithmic scale.
Source CorrelationIn this small indicator I make it possible for the user to set two different input sources. Then, the indicator displays the correlation of these two input sources. It's a very small script, but I think it could be helpful to somebody to find uncorrelated indicators for his trading strategy. To use uncorrelated indicators is in general recommended.
Enjoy this small, but powerful tool. 🧙♂️
Correlation Coefficient - DXY & XAUPublishing my first indicator on TradingView. Essentially a modification of the Correlation Coefficient indicator, that displays a 2 ticker symbols' correlation coefficient vs, the chart presently loaded.. You can modify the symbols, but the default uses DXY and XAU, which have been displaying strong negative correlation.
As with the built-in CC (Correlation Coefficient) indicator, readings are taken the same way:
Positive Correlation = anything above 0 | stronger as it moves up towards 1 | weaker as it moves back down towards 0
Negative Correlation = anything below 0 | stronger moving down towards -1 | weaker moving back up towards 0
This is primarily created to work with the Bitcoin weekly chart, for comparing DXY and Gold (XAU) price correlations (in advance, when possible). If you change the chart timeframe to something other than weekly, consider playing with the Length input, which is set to 35 by default where I think it best represents correlations with Bitcoin's weekly timeframe for DXY and Gold.
The intention is that you might be able to determine future direction of Bitcoin based on positive or negative correlations of Gold and/or the US Dollar Index. DXY has been making peaks and valleys prior to Bitcoin since after March 2020 black swan event, where it peaked just after instead. In the future, it may flip over again and Bitcoin may hit major highs or lows prior to DXY, again. So, keep an eye on the charts for all 3, as well as the indicator correlations.
Currently, we've moved back into negative correlation between Bitcoin and DXY, and positive correlation with Bitcoin and Gold:
Negative Correlation b/w Bitcoin and DXY - if DXY moves up, Bitcoin likely moves down, or if DXY moves down, Bitcoin likely moves up (or if Bitcoin were to move first before DXY, as it did on March 2020, instead)
Positive Correlation b/w Bitcoin and Gold - Bitcoin and Gold will likely move up or down with each other.
DXY is represented by the green histogram and label, Gold is represented by the yellow histogram and label. Again, you can modify the tickers you want to check against, and you can modify the colors for their histograms / labels.
The inspiration from came from noticing areas of same date or delayed negative correlation between Bitcoin and DXY, here is one of my most recent posts about that:
Please let me know if you have any questions, or would like to see updates to the indicator to make it easier to use or add more useful features to it.
I hope this becomes useful to you in some way. Thank you for your support!
Cheers,
dudebruhwhoa :)
MA Correlation CoefficientThis script helps you visualize the correlation between the price of an asset and 4 moving averages of your choice. This indicator can help you identify trendy markets as well as trend-shifts.
Disclaimer
Bear in mind that there is always some lag when using Moving-Averages, hence the purpose of this indicator is as a trend identification tool rather than an entry-exit strategy.
Working Principle
The basic idea behind this indicator is the following:
In a trendy market you will find high correlation between price and all kinds of Moving-Averages. This works both ways, no matter bull or bear trend.
In sideways markets you might find a mix of correlations accross timeframes (2018) or high correlation with Low-Timeframe averages and low correlation with High-Timeframe averages (2021/2022).
Trend shifts might be characterised by a 'staircase' type of correlation (yellow), where the asset regains correlation with higher timeframe averages
Indicator Options
1. Source : data used for indicator calculation
1. Correlation Window : size of moving window for correlation calculation
2. Average Type :
Simple-Moving-Average (SMA)
Exponential-Moving-Average (EMA)
Hull-Moving-Average (HMA)
Volume-Weighted-Moving-Average (VWMA)
3. Lookback : number of past candles to calculate average
4. Gradient : modify gradient colors. colors relate to correlation values.
Plot Explanation
The indicator plots, using colors, the correlation of the asset with 4 averages. For every candle, 4 correlation values are generated, corresponding to 4 colors. These 4 colors are stacked one on top of the other generating the patterns explained above. These patterns may help you identify what kind of market you're in.
Crypto Correlation MatrixA crypto correlation matrix or table is a tool that displays the correlation between different cryptocurrencies and other financial assets. The matrix provides an overview of the degree to which various cryptocurrencies move in tandem or independently of each other. Each cell represents the correlation between the row and column assets respectively.
The correlation matrix can be useful for traders and investors in several ways:
First, it allows them to identify trends and patterns in the behavior of different cryptocurrencies. By looking at the correlations between different assets, traders can gain insight into the intra-relationships of the crypto market and make more informed trading decisions. For example, if two cryptocurrencies have a high positive correlation, meaning that they tend to move in the same direction, a trader may want to diversify their portfolio by choosing to invest in only one of the two assets.
Additionally, the correlation matrix can help traders and investors to manage risk. By analyzing the correlations between different assets, traders can identify opportunities to hedge their positions or limit their exposure to particular risks. For example, if a trader holds a portfolio of cryptocurrencies that are highly correlated with each other, they may be at greater risk of losses if the market moves against them. By diversifying their portfolio with assets that are less correlated with each other, they can reduce their overall risk.
Some of the unique properties for this specific script are the correlation strength levels in conjunction with the color gradient of cells, intended for clearer readability.
Features:
Supports up to 64 different crypto assets.
Dark/Light mode.
Correlation strength levels and cell coloring.
Adjustable positioning on the chart.
Alerts at the close of a bar. (Daily timeframe or higher recommended)
loxxfftLibrary "loxxfft"
This code is a library for performing Fast Fourier Transform (FFT) operations. FFT is an algorithm that can quickly compute the discrete Fourier transform (DFT) of a sequence. The library includes functions for performing FFTs on both real and complex data. It also includes functions for fast correlation and convolution, which are operations that can be performed efficiently using FFTs. Additionally, the library includes functions for fast sine and cosine transforms.
Reference:
www.alglib.net
fastfouriertransform(a, nn, inversefft)
Returns Fast Fourier Transform
Parameters:
a (float ) : float , An array of real and imaginary parts of the function values. The real part is stored at even indices, and the imaginary part is stored at odd indices.
nn (int) : int, The number of function values. It must be a power of two, but the algorithm does not validate this.
inversefft (bool) : bool, A boolean value that indicates the direction of the transformation. If True, it performs the inverse FFT; if False, it performs the direct FFT.
Returns: float , Modifies the input array a in-place, which means that the transformed data (the FFT result for direct transformation or the inverse FFT result for inverse transformation) will be stored in the same array a after the function execution. The transformed data will have real and imaginary parts interleaved, with the real parts at even indices and the imaginary parts at odd indices.
realfastfouriertransform(a, tnn, inversefft)
Returns Real Fast Fourier Transform
Parameters:
a (float ) : float , A float array containing the real-valued function samples.
tnn (int) : int, The number of function values (must be a power of 2, but the algorithm does not validate this condition).
inversefft (bool) : bool, A boolean flag that indicates the direction of the transformation (True for inverse, False for direct).
Returns: float , Modifies the input array a in-place, meaning that the transformed data (the FFT result for direct transformation or the inverse FFT result for inverse transformation) will be stored in the same array a after the function execution.
fastsinetransform(a, tnn, inversefst)
Returns Fast Discrete Sine Conversion
Parameters:
a (float ) : float , An array of real numbers representing the function values.
tnn (int) : int, Number of function values (must be a power of two, but the code doesn't validate this).
inversefst (bool) : bool, A boolean flag indicating the direction of the transformation. If True, it performs the inverse FST, and if False, it performs the direct FST.
Returns: float , The output is the transformed array 'a', which will contain the result of the transformation.
fastcosinetransform(a, tnn, inversefct)
Returns Fast Discrete Cosine Transform
Parameters:
a (float ) : float , This is a floating-point array representing the sequence of values (time-domain) that you want to transform. The function will perform the Fast Cosine Transform (FCT) or the inverse FCT on this input array, depending on the value of the inversefct parameter. The transformed result will also be stored in this same array, which means the function modifies the input array in-place.
tnn (int) : int, This is an integer value representing the number of data points in the input array a. It is used to determine the size of the input array and control the loops in the algorithm. Note that the size of the input array should be a power of 2 for the Fast Cosine Transform algorithm to work correctly.
inversefct (bool) : bool, This is a boolean value that controls whether the function performs the regular Fast Cosine Transform or the inverse FCT. If inversefct is set to true, the function will perform the inverse FCT, and if set to false, the regular FCT will be performed. The inverse FCT can be used to transform data back into its original form (time-domain) after the regular FCT has been applied.
Returns: float , The resulting transformed array is stored in the input array a. This means that the function modifies the input array in-place and does not return a new array.
fastconvolution(signal, signallen, response, negativelen, positivelen)
Convolution using FFT
Parameters:
signal (float ) : float , This is an array of real numbers representing the input signal that will be convolved with the response function. The elements are numbered from 0 to SignalLen-1.
signallen (int) : int, This is an integer representing the length of the input signal array. It specifies the number of elements in the signal array.
response (float ) : float , This is an array of real numbers representing the response function used for convolution. The response function consists of two parts: one corresponding to positive argument values and the other to negative argument values. Array elements with numbers from 0 to NegativeLen match the response values at points from -NegativeLen to 0, respectively. Array elements with numbers from NegativeLen+1 to NegativeLen+PositiveLen correspond to the response values in points from 1 to PositiveLen, respectively.
negativelen (int) : int, This is an integer representing the "negative length" of the response function. It indicates the number of elements in the response function array that correspond to negative argument values. Outside the range , the response function is considered zero.
positivelen (int) : int, This is an integer representing the "positive length" of the response function. It indicates the number of elements in the response function array that correspond to positive argument values. Similar to negativelen, outside the range , the response function is considered zero.
Returns: float , The resulting convolved values are stored back in the input signal array.
fastcorrelation(signal, signallen, pattern, patternlen)
Returns Correlation using FFT
Parameters:
signal (float ) : float ,This is an array of real numbers representing the signal to be correlated with the pattern. The elements are numbered from 0 to SignalLen-1.
signallen (int) : int, This is an integer representing the length of the input signal array.
pattern (float ) : float , This is an array of real numbers representing the pattern to be correlated with the signal. The elements are numbered from 0 to PatternLen-1.
patternlen (int) : int, This is an integer representing the length of the pattern array.
Returns: float , The signal array containing the correlation values at points from 0 to SignalLen-1.
tworealffts(a1, a2, a, b, tn)
Returns Fast Fourier Transform of Two Real Functions
Parameters:
a1 (float ) : float , An array of real numbers, representing the values of the first function.
a2 (float ) : float , An array of real numbers, representing the values of the second function.
a (float ) : float , An output array to store the Fourier transform of the first function.
b (float ) : float , An output array to store the Fourier transform of the second function.
tn (int) : float , An integer representing the number of function values. It must be a power of two, but the algorithm doesn't validate this condition.
Returns: float , The a and b arrays will contain the Fourier transform of the first and second functions, respectively. Note that the function overwrites the input arrays a and b.
█ Detailed explaination of each function
Fast Fourier Transform
The fastfouriertransform() function takes three input parameters:
1. a: An array of real and imaginary parts of the function values. The real part is stored at even indices, and the imaginary part is stored at odd indices.
2. nn: The number of function values. It must be a power of two, but the algorithm does not validate this.
3. inversefft: A boolean value that indicates the direction of the transformation. If True, it performs the inverse FFT; if False, it performs the direct FFT.
The function performs the FFT using the Cooley-Tukey algorithm, which is an efficient algorithm for computing the discrete Fourier transform (DFT) and its inverse. The Cooley-Tukey algorithm recursively breaks down the DFT of a sequence into smaller DFTs of subsequences, leading to a significant reduction in computational complexity. The algorithm's time complexity is O(n log n), where n is the number of samples.
The fastfouriertransform() function first initializes variables and determines the direction of the transformation based on the inversefft parameter. If inversefft is True, the isign variable is set to -1; otherwise, it is set to 1.
Next, the function performs the bit-reversal operation. This is a necessary step before calculating the FFT, as it rearranges the input data in a specific order required by the Cooley-Tukey algorithm. The bit-reversal is performed using a loop that iterates through the nn samples, swapping the data elements according to their bit-reversed index.
After the bit-reversal operation, the function iteratively computes the FFT using the Cooley-Tukey algorithm. It performs calculations in a loop that goes through different stages, doubling the size of the sub-FFT at each stage. Within each stage, the Cooley-Tukey algorithm calculates the butterfly operations, which are mathematical operations that combine the results of smaller DFTs into the final DFT. The butterfly operations involve complex number multiplication and addition, updating the input array a with the computed values.
The loop also calculates the twiddle factors, which are complex exponential factors used in the butterfly operations. The twiddle factors are calculated using trigonometric functions, such as sine and cosine, based on the angle theta. The variables wpr, wpi, wr, and wi are used to store intermediate values of the twiddle factors, which are updated in each iteration of the loop.
Finally, if the inversefft parameter is True, the function divides the result by the number of samples nn to obtain the correct inverse FFT result. This normalization step is performed using a loop that iterates through the array a and divides each element by nn.
In summary, the fastfouriertransform() function is an implementation of the Cooley-Tukey FFT algorithm, which is an efficient algorithm for computing the DFT and its inverse. This FFT library can be used for a variety of applications, such as signal processing, image processing, audio processing, and more.
Feal Fast Fourier Transform
The realfastfouriertransform() function performs a fast Fourier transform (FFT) specifically for real-valued functions. The FFT is an efficient algorithm used to compute the discrete Fourier transform (DFT) and its inverse, which are fundamental tools in signal processing, image processing, and other related fields.
This function takes three input parameters:
1. a - A float array containing the real-valued function samples.
2. tnn - The number of function values (must be a power of 2, but the algorithm does not validate this condition).
3. inversefft - A boolean flag that indicates the direction of the transformation (True for inverse, False for direct).
The function modifies the input array a in-place, meaning that the transformed data (the FFT result for direct transformation or the inverse FFT result for inverse transformation) will be stored in the same array a after the function execution.
The algorithm uses a combination of complex-to-complex FFT and additional transformations specific to real-valued data to optimize the computation. It takes into account the symmetry properties of the real-valued input data to reduce the computational complexity.
Here's a detailed walkthrough of the algorithm:
1. Depending on the inversefft flag, the initial values for ttheta, c1, and c2 are determined. These values are used for the initial data preprocessing and post-processing steps specific to the real-valued FFT.
2. The preprocessing step computes the initial real and imaginary parts of the data using a combination of sine and cosine terms with the input data. This step effectively converts the real-valued input data into complex-valued data suitable for the complex-to-complex FFT.
3. The complex-to-complex FFT is then performed on the preprocessed complex data. This involves bit-reversal reordering, followed by the Cooley-Tukey radix-2 decimation-in-time algorithm. This part of the code is similar to the fastfouriertransform() function you provided earlier.
4. After the complex-to-complex FFT, a post-processing step is performed to obtain the final real-valued output data. This involves updating the real and imaginary parts of the transformed data using sine and cosine terms, as well as the values c1 and c2.
5. Finally, if the inversefft flag is True, the output data is divided by the number of samples (nn) to obtain the inverse DFT.
The function does not return a value explicitly. Instead, the transformed data is stored in the input array a. After the function execution, you can access the transformed data in the a array, which will have the real part at even indices and the imaginary part at odd indices.
Fast Sine Transform
This code defines a function called fastsinetransform that performs a Fast Discrete Sine Transform (FST) on an array of real numbers. The function takes three input parameters:
1. a (float array): An array of real numbers representing the function values.
2. tnn (int): Number of function values (must be a power of two, but the code doesn't validate this).
3. inversefst (bool): A boolean flag indicating the direction of the transformation. If True, it performs the inverse FST, and if False, it performs the direct FST.
The output is the transformed array 'a', which will contain the result of the transformation.
The code starts by initializing several variables, including trigonometric constants for the sine transform. It then sets the first value of the array 'a' to 0 and calculates the initial values of 'y1' and 'y2', which are used to update the input array 'a' in the following loop.
The first loop (with index 'jx') iterates from 2 to (tm + 1), where 'tm' is half of the number of input samples 'tnn'. This loop is responsible for calculating the initial sine transform of the input data.
The second loop (with index 'ii') is a bit-reversal loop. It reorders the elements in the array 'a' based on the bit-reversed indices of the original order.
The third loop (with index 'ii') iterates while 'n' is greater than 'mmax', which starts at 2 and doubles each iteration. This loop performs the actual Fast Discrete Sine Transform. It calculates the sine transform using the Danielson-Lanczos lemma, which is a divide-and-conquer strategy for calculating Discrete Fourier Transforms (DFTs) efficiently.
The fourth loop (with index 'ix') is responsible for the final phase adjustments needed for the sine transform, updating the array 'a' accordingly.
The fifth loop (with index 'jj') updates the array 'a' one more time by dividing each element by 2 and calculating the sum of the even-indexed elements.
Finally, if the 'inversefst' flag is True, the code scales the transformed data by a factor of 2/tnn to get the inverse Fast Sine Transform.
In summary, the code performs a Fast Discrete Sine Transform on an input array of real numbers, either in the direct or inverse direction, and returns the transformed array. The algorithm is based on the Danielson-Lanczos lemma and uses a divide-and-conquer strategy for efficient computation.
Fast Cosine Transform
This code defines a function called fastcosinetransform that takes three parameters: a floating-point array a, an integer tnn, and a boolean inversefct. The function calculates the Fast Cosine Transform (FCT) or the inverse FCT of the input array, depending on the value of the inversefct parameter.
The Fast Cosine Transform is an algorithm that converts a sequence of values (time-domain) into a frequency domain representation. It is closely related to the Fast Fourier Transform (FFT) and can be used in various applications, such as signal processing and image compression.
Here's a detailed explanation of the code:
1. The function starts by initializing a number of variables, including counters, intermediate values, and constants.
2. The initial steps of the algorithm are performed. This includes calculating some trigonometric values and updating the input array a with the help of intermediate variables.
3. The code then enters a loop (from jx = 2 to tnn / 2). Within this loop, the algorithm computes and updates the elements of the input array a.
4. After the loop, the function prepares some variables for the next stage of the algorithm.
5. The next part of the algorithm is a series of nested loops that perform the bit-reversal permutation and apply the FCT to the input array a.
6. The code then calculates some additional trigonometric values, which are used in the next loop.
7. The following loop (from ix = 2 to tnn / 4 + 1) computes and updates the elements of the input array a using the previously calculated trigonometric values.
8. The input array a is further updated with the final calculations.
9. In the last loop (from j = 4 to tnn), the algorithm computes and updates the sum of elements in the input array a.
10. Finally, if the inversefct parameter is set to true, the function scales the input array a to obtain the inverse FCT.
The resulting transformed array is stored in the input array a. This means that the function modifies the input array in-place and does not return a new array.
Fast Convolution
This code defines a function called fastconvolution that performs the convolution of a given signal with a response function using the Fast Fourier Transform (FFT) technique. Convolution is a mathematical operation used in signal processing to combine two signals, producing a third signal representing how the shape of one signal is modified by the other.
The fastconvolution function takes the following input parameters:
1. float signal: This is an array of real numbers representing the input signal that will be convolved with the response function. The elements are numbered from 0 to SignalLen-1.
2. int signallen: This is an integer representing the length of the input signal array. It specifies the number of elements in the signal array.
3. float response: This is an array of real numbers representing the response function used for convolution. The response function consists of two parts: one corresponding to positive argument values and the other to negative argument values. Array elements with numbers from 0 to NegativeLen match the response values at points from -NegativeLen to 0, respectively. Array elements with numbers from NegativeLen+1 to NegativeLen+PositiveLen correspond to the response values in points from 1 to PositiveLen, respectively.
4. int negativelen: This is an integer representing the "negative length" of the response function. It indicates the number of elements in the response function array that correspond to negative argument values. Outside the range , the response function is considered zero.
5. int positivelen: This is an integer representing the "positive length" of the response function. It indicates the number of elements in the response function array that correspond to positive argument values. Similar to negativelen, outside the range , the response function is considered zero.
The function works by:
1. Calculating the length nl of the arrays used for FFT, ensuring it's a power of 2 and large enough to hold the signal and response.
2. Creating two new arrays, a1 and a2, of length nl and initializing them with the input signal and response function, respectively.
3. Applying the forward FFT (realfastfouriertransform) to both arrays, a1 and a2.
4. Performing element-wise multiplication of the FFT results in the frequency domain.
5. Applying the inverse FFT (realfastfouriertransform) to the multiplied results in a1.
6. Updating the original signal array with the convolution result, which is stored in the a1 array.
The result of the convolution is stored in the input signal array at the function exit.
Fast Correlation
This code defines a function called fastcorrelation that computes the correlation between a signal and a pattern using the Fast Fourier Transform (FFT) method. The function takes four input arguments and modifies the input signal array to store the correlation values.
Input arguments:
1. float signal: This is an array of real numbers representing the signal to be correlated with the pattern. The elements are numbered from 0 to SignalLen-1.
2. int signallen: This is an integer representing the length of the input signal array.
3. float pattern: This is an array of real numbers representing the pattern to be correlated with the signal. The elements are numbered from 0 to PatternLen-1.
4. int patternlen: This is an integer representing the length of the pattern array.
The function performs the following steps:
1. Calculate the required size nl for the FFT by finding the smallest power of 2 that is greater than or equal to the sum of the lengths of the signal and the pattern.
2. Create two new arrays a1 and a2 with the length nl and initialize them to 0.
3. Copy the signal array into a1 and pad it with zeros up to the length nl.
4. Copy the pattern array into a2 and pad it with zeros up to the length nl.
5. Compute the FFT of both a1 and a2.
6. Perform element-wise multiplication of the frequency-domain representation of a1 and the complex conjugate of the frequency-domain representation of a2.
7. Compute the inverse FFT of the result obtained in step 6.
8. Store the resulting correlation values in the original signal array.
At the end of the function, the signal array contains the correlation values at points from 0 to SignalLen-1.
Fast Fourier Transform of Two Real Functions
This code defines a function called tworealffts that computes the Fast Fourier Transform (FFT) of two real-valued functions (a1 and a2) using a Cooley-Tukey-based radix-2 Decimation in Time (DIT) algorithm. The FFT is a widely used algorithm for computing the discrete Fourier transform (DFT) and its inverse.
Input parameters:
1. float a1: an array of real numbers, representing the values of the first function.
2. float a2: an array of real numbers, representing the values of the second function.
3. float a: an output array to store the Fourier transform of the first function.
4. float b: an output array to store the Fourier transform of the second function.
5. int tn: an integer representing the number of function values. It must be a power of two, but the algorithm doesn't validate this condition.
The function performs the following steps:
1. Combine the two input arrays, a1 and a2, into a single array a by interleaving their elements.
2. Perform a 1D FFT on the combined array a using the radix-2 DIT algorithm.
3. Separate the FFT results of the two input functions from the combined array a and store them in output arrays a and b.
Here is a detailed breakdown of the radix-2 DIT algorithm used in this code:
1. Bit-reverse the order of the elements in the combined array a.
2. Initialize the loop variables mmax, istep, and theta.
3. Enter the main loop that iterates through different stages of the FFT.
a. Compute the sine and cosine values for the current stage using the theta variable.
b. Initialize the loop variables wr and wi for the current stage.
c. Enter the inner loop that iterates through the butterfly operations within each stage.
i. Perform the butterfly operation on the elements of array a.
ii. Update the loop variables wr and wi for the next butterfly operation.
d. Update the loop variables mmax, istep, and theta for the next stage.
4. Separate the FFT results of the two input functions from the combined array a and store them in output arrays a and b.
At the end of the function, the a and b arrays will contain the Fourier transform of the first and second functions, respectively. Note that the function overwrites the input arrays a and b.
█ Example scripts using functions contained in loxxfft
Real-Fast Fourier Transform of Price w/ Linear Regression
Real-Fast Fourier Transform of Price Oscillator
Normalized, Variety, Fast Fourier Transform Explorer
Variety RSI of Fast Discrete Cosine Transform
STD-Stepped Fast Cosine Transform Moving Average
Rsi strategy for BTC with (Rsi SPX)
I hope this strategy is just an idea and a starting point, I use the correlation of the Sp500 with the Btc, this does not mean that this correlation will exist forever!. I love Trading view and I'm learning to program, I find correlations very interesting and here is a simple strategy.
This is a trading strategy script written in Pine Script language for use in TradingView. Here is a brief overview of the strategy:
The script uses the RSI (Relative Strength Index) technical indicator with a period of 14 on two securities: the S&P 500 (SPX) and the symbol corresponding to the current chart (presumably Bitcoin, based on the variable name "Btc_1h_fixed"). The RSI is plotted on the chart for both securities.
The script then sets up two trading conditions using the RSI values:
A long entry condition: when the RSI for the current symbol crosses above the RSI for the S&P 500, a long trade is opened using the "strategy.entry" function.
A short entry condition: when the RSI for the current symbol crosses below the RSI for the S&P 500, a short trade is opened using the "strategy.entry" function.
The script also includes a take profit input parameter that allows the user to set a percentage profit target for closing the trade. The take profit is set using the "strategy.exit" function.
Overall, the strategy aims to take advantage of divergences in RSI values between the current symbol and the S&P 500 by opening long or short trades accordingly. The take profit parameter allows the user to set a specific profit target for each trade. However, the script does not include any stop loss or risk management features, which should be considered when implementing the strategy in a real trading scenario.
Stock Data Table█ OVERVIEW
This is a table that shows some information about stocks. It is divided into four sections:
1) Correlation
2) Shares
3) Daily Data
4) Extended Session Data
The table is completely modular, which means you can add or remove each element from the settings menu, and it will automatically rearrange its spaces.
It is also highly customizable, to the extent that you can change almost any color, remove or change titles, invert section rows, and much more.
1) Correlation
The script checks if the stock is listed on NASDAQ, and if so, uses the QQQ (Nasdaq-100 ETF) as the reference index in the first cell; otherwise, it uses the SPY (S&P 500 ETF). The length of the correlation is shown in the second cell. The table then displays the correlation between the reference index and the other index, and the correlation between the reference index and the stock.
To make it easier to interpret the correlation values, each row's last cell is color-coded with a gradient to highlight the type of correlation, and the direction of the gradient can be customized.
The correlation coefficient is a statistical measure that quantifies the strength and direction of the relationship between two variables, indicating how changes in one variable are associated with changes in the other variable, so it can be used to identify patterns and trends.
If you are interested in correlation, I suggest taking a look at my dedicated indicator:
2) Shares
This feature provides you with quick access to key information about shares and market capitalization.
On one row, you can view the total shares outstanding and the market capitalization for the fiscal year or the quarterly year. The total shares outstanding represents the total number of shares of the stock that have been issued and are currently outstanding, regardless of whether they are held by insiders or public investors. The market capitalization is a widely used measure of the company's value as determined by the stock market, calculated by multiplying its current stock price with the total number of outstanding shares.
The other row shows the float, which is the number of shares of a company that are available for public trading, and the corresponding free-float market cap, calculated by multiplying the company's current stock price with the float. Because Pine Script does not allow retrieving information about quarterly year float, you can view the float and the free-float market cap of the fiscal year only. The data can be displayed at all times or only when the difference between the total shares outstanding and the float is significant enough to result in a difference between the market cap and free-float market cap.
The classification for market cap and free-float market cap is set in this way:
Mega Cap: $200 billion or more
Large Cap: between $10 billion and $200 billion
Mid Cap: between $2 billion and $10 billion
Small Cap: between $300 million and $2 billion
Micro Cap: less than $300 million
Penny Stocks: less than $5 (customizable)
Comparing the free-float market cap to the market cap can provide insights into the liquidity of a stock. In fact, if the float is relatively small compared to the total shares outstanding, it may be more difficult to find buyers or sellers, which could lead to increased volatility. On the other hand, a larger float indicates that the stock is more liquid and may be easier to trade, potentially resulting in lower volatility. However, market conditions can change quickly and significantly, especially for intraday traders, and the free-float can also change as insiders or other large shareholders buy or sell shares. Therefore, comparing the data of the fiscal year with that of the quarterly year may not provide the most up-to-date and accurate information for making trading decisions. This limitation can be mitigated by combining those data with other indicators and tools, such as technical analysis or news events, to gain a better understand of the stock's performance and potential trading opportunities.
3) Daily Data
This section is available on daily charts only due to the lack of accuracy of real-time daily data on other time frames. Here, you can view the Average Daily Volume (ADV) over a preferred time range (20 days by default), and the Daily Change, which represents the percentage difference between the closing price on two consecutive trading days.
ADV is useful in measuring the stock's volatility, as it provides an indication of how much trading activity there is in it. Generally speaking, stocks with higher trading volume tend to be less volatile than stocks with lower trading volume. High trading volume means there are more buyers and sellers actively trading the stock, which makes it easier for investors to buy and sell shares at fair prices. This increased liquidity can help to stabilize the stock price, reducing the potential for large swings in either direction. On the other hand, stocks with lower trading volume may experience greater volatility, as there are fewer buyers and sellers actively trading the stock. This can result in larger price swings, as it may be more difficult for investors to buy or sell shares at fair prices.
The daily percentage change can provide an indication of the stock's volatility, with larger values indicating greater volatility and risk. It can also be compared to that of a benchmark such an index or other stocks in the same sector, helping to determine whether the stock is outperforming or underperforming relative to them.
4) Extended Session Data
The fourth section is available on intraday charts only. This section provides two pieces of information: the Extended Session Change and the Pre-Market Volume.
The Extended Session Change indicates the percentage difference between the previous day's closing price and the latest price in the extended session. This gives you the extent and the direction of the price gap that occurred during extended trading hours.
The Pre-Market Volume shows the sum of all shares traded during the pre-market session. This can be helpful in understanding how much interest the stock gained before the market opened.
By default, the two rows will be visible at all times. They will stop updating after the end of their respective time range, and resume updating when it starts again. However, you can choose to automatically hide them outside of their time ranges.
Both the extended session and pre-market time ranges can be customized. Please note that if you select time ranges outside of the regular market session (as set by default), you must enable the extended session to view the corresponding rows.
█ GENERAL NOTES
• Total Shares Outstanding, Float, Average Daily Volume and Pre-Market Volume cells use a customizable color system based on two thresholds, to help you quickly identify whether the value is "too low/acceptable/too high" or "too low/not enough high/acceptable".
• If you cannot see certain data, that simply means it is not available.
Bitcoin Correlation MapHello everyone,
This indicator shows the correlation coefficients of altcoins with bitcoin in a table.
What is the correlation coefficient?
The correlation coefficient is a value that takes a value between 0 and 1 when a parity makes similar movements with the reference parity, and takes a value between 0 and -1 when it makes opposite movements.
In order to obtain more meaningful and real-time results in this indicator, the weighted average of the correlation values of the last 200bar was used. You can change the bar length as you wish. With the correlation value, you can see the parities that have similar movements with bitcoin and integrate them into your strategy.
You can change the coin list as you wish, and you can also calculate their correlation with etherium instead of bitcoin .
The indicator shows the correlation value of 36 altcoins at the moment.
The indicator indicates the color of the correlated parities as green and the color of the inversely correlated parities as red.
Cheers
Correlation Coefficient: Visible Range Dynamic Average R -Correlation Coefficient with Dynamic Average R (shows R average for the visible chart only, changes as you zoom in or out)
-Label: Vis-Avg-R = Visable Average R
-the Correlation Coefficient function for Pearson's R is taken from "BA🐷 CC" indicator by @balipour (highly recommended; more thorough treatment of R and other stats, but without the dynamic average)
-I wrote this primarily to add a dynamic Average R, showing correlation for arbitrary start times/end times; whether it be the last month, last year, of some specific period from the past (backtest mode)
-I have been using this to get an idea of correlation regimes over time between Bonds vs Stocks (ZB1! vs ES1!).
-As you see from the above, most of 2022 has seen an unusually strong positive correlation between Bonds and Stocks
~~inputs:
-lookback length for calculation of R
-Backtest mode (true by default): displays Average R for ONLY the visible range displayed on any part of chart history (LHS to RHS of screen only)
-source for both Ticker and compared Asset (close, open, high, low, ohlc4.. etc)
~~some other assets worth comparing:
Aussie vs Gold; Aussie vs ES; Btc vs ES; Copper vs ES
Correlated ATR MA | AdulariHow do I use it?
Never use this indicator as standalone trading signal, it should be used as confluence.
When the price is above the moving average this shows the bullish trend is strong.
When the price is below the moving average this shows the bearish trend is strong.
When the moving average is purple, the trend is bullish, when it is gray, the trend is bearish.
Features:
Purple line for bullish trend and gray line for bearish trend.
Custom formula combining an ATR and Hull MA to clearly indicate trend strength and direction.
Unique approach to moving averages by taking the average of 3 types of MA's combined with custom ATR's.
How does it work?
1 — ATR value is calculated, then the correlation between the source and ATR is calculated.
2 — Signal value is calculated from the difference between the previous source and ATR values.
3 — Final value is being calculated using the following formula:
cor * target + (1 - cor) * nz(atr , target)
4 — Moving average is calculated by getting the average of 3 values: a normal HMA, HMA plus final value, and HMA minus final value.
Multi Delta-Agnostic Correlation Coefficient (tartigradia)Display three DACC plots simultaneously, to visualize both directional (up on top, down at bottom) and adirectional DACC (in the middle) simultaneously.
Delta Agnostic Correlation calculates a correlation between two symbols based only on the sign of their changes using a Sign Test (en.m.wikipedia.org), regardless of the amplitude of price change. Compared to a standard Pearson correlation (quantitative test), Sign Test correlations (discrete test) are highly sensitive to directional change with 0 lag, at the expense of lacking sensitivity to quantity correlation (ie, it does not matter if changes are big or small).
Hence, this Delta-Agnostic Correlation Coefficient (DCC or DACC) indicator is better used to detect early changes in correlations, and then confirmation with a typical Pearson correlation or a non-parametric Spearman test or Mutual Information (all three are quantitative tests, hence accounting for quantity and not just direction) can allow to be more sensitive to quantities too and hence be a robust combination to demonstrate strong correlations both in direction and amplitude.
Adequate statistical significance testing, using a two-sided binomial statistical test, is also implemented. Note however that one assumption of the sign test may here be violated: independence of observations for each symbol. If you assume the market is not acting on a random walk, then there is a temporal autocorrelation, and this biases the sign test. However, in practice, the test works well enough.
The directional variants of the test allow to test the correlation hypothesis only if the index symbol goes into one direction. For example, if we suspect that the index symbol is correlated with the current symbol but only when the index symbol is bullish, we can select "Up" to test this hypothesis. Note that given the specificities of how directional and adirectional tests differ in how they work, the default fill is different: zero-value fill for adirectional test to simulate how price action tend to lose momentum during market close periods, previous DCC_MA (= no change in DCC value) during both market close periods and when the direction is opposite for the directional variants of the test, so that while the market is moving opposite, we don't lose the statistical significance built up to now, otherwise it would be nonsensical (for the directional tests).
For more information on the theory behind, see the original DACC indicator, which is the same script but with only one plot:
Volatility Inverse Correlation CandleThis is an educational tool that can help you find direct or inverse relations between two assets.
In this case I am using VIX and SPX .
The way it works is the next one :
So I am looking at the current open value of VIX in comparison with the previous close ( if it either above or below) and after on the SPX I am looking into the history and see for example which type of candle we had in respect with the opening value from VIX .
So for example, lets imagine that today is monday, and the weekly open value from VIX was higher than previous friday close value. Now I am going to see with the inverse correlation , if based on this idea, the current weekly candle from SPX finished in a bear candle.
The same can be applied for the bearish situation, so if we had an open from VIX lower than previous close, we are looking to check the SPX bull candle accuracy.
At the same time, for a different type of calculation I have added an internal lookup into heikin ashi values.
If you have any questions please let me know !
[PlayBit]Correlation-Co _OI Correlation-Co _OI
This Indicator uses a Correlation Coefficient to compare a Crypto Currency to the Binance Open Interest feed if the data is provided
A move in the same direction is indicated with a positive value (the indicator will move up)
A move in the opposite direction the indicator will indicate with a negative value (the indicator will move down)
If both are moving in the same direction and are converging or diverging this will be shown by larger values for divergence and smaller for convergence but will be a positive value
Negative values are shown when price and _OI are moving opposite each other
You can toggle the auto Open Interest option in the settings to use something other than Open Interest if you would like
I still need to add a visual showing when longs are unwinding or opening and when shorts are covering or opening
This is a concept that I made for @Johnny a while back and I'm republishing public from private
This can be useful when comparing a Asset with its Open Interest
The main bit of code was taken from:
by @mortdiggiddy
Let me know if you have any Ideas or suggestions or if I overlooked something
Hope you enjoy,
@FFriZz | @FrizLabz
SpreadTrade - Auto-Cointegration (ps5)Decsription: Auto-Cointegration-Based Pair Trading Strategy (revised version)
To review, there are three popular styles of Pair trading: distance-based pair trading, correlation-based pair trading and cointegration-based pair trading. Typically, they require preliminary statistical estimation of the viability of the corresponding strategy.
Basically a pair trade strategy boils down to shorting the outperforming instrument and going long on the underperforming instrument whenever the temporary correlation weakens which means one instrument is going up and another is going down. Apart from the typical cointegration strategy which employs two cointegrated instruments, this script uses just one instrument, in base timeframe and in lagged timeframe, actually making it an auto-cointegration, or better still, an auto-correlation strategy.
Notice that each moving average function may require different Threshold settings.The orange cross symbol indicates the exit points. To filter out the signals use higher values for the LongWindow and the Threshold parameters. Also pay attention that in some cases with some moving averages the color of the signals has to be inverted.
Correlation ZonesThis indicator highlights zones with strong, weak and negative correlation. Unlike standard coefficient indicator it will help to filter out noise when analyzing dependencies between two assets.
With default input setting Correlation_Threshold=0.5:
- Zones with correlation above 0.5, will be colored in green (strong correlation)
- Zones with correlation from -0.5 to 0.5 will be colored grey (weak correlation)
- Zones with correlation below -0.5 will be colore red (strong negative correlation)
Input parameter "Correlation_Threshold" can be modified in settings.
Provided example demonstrates BTCUSD correlation with NASDAQ Composite . I advice to use weekly timeframe and set length to 26 week for this study
Kendall Rank Correlation Coefficient (alt)This is a non-parametric correlation statistical test, which is less sensitive to magnitude and more to direction, hence why some people call this a "concordance test".
This indicator was originally created by Alex Orekhov (everget), if you like this one, please show the original author some love:
This version is extended by tartigradia (2022) to make it more readily useable:
* Update to pinescript v5
* Default compare to current symbol (instead of only fixed symbols)
* Add 1.0, 0.0 and -1.0 correlation levels lines.
This indicator plots both the Kendall correlation in orange, and the more classical parametric Pearson correlation in purple for comparison. Either can be disabled in the Style tab.
Correlation with P-Value & Confidence Interval (alt)Shows the Pearson correlation between two symbols, including statistical significance test.
This is a fork of the original script by Balipour, with the addition of EMA that can be used instead of SMA in the Pearson correlation as an attempt to capture correlation trend changes more quickly, and conversion to pinescript v5. In the end, the EMA does not help much, for a faster capture of correlation trend changes, another kind of correlation is necessary, such as sign test correlation (another one of my indicators implement this idea).
Please show the original indicator's author some love if you appreciate this work:
Delta-Agnostic Correlation Coefficient (alt)Calculate a sort of correlation between two symbols based only on the sign of their changes, regardless of the amplitude of price change.
When positive, the two symbols tend to move together. When negative, the symbols move in opposite directions.
Since there is no significance calculation, and that the result is binary, keep in mind that correlation will always tend to go towards 1 or -1 even when there is no correlation. To reduce this issue, an EMA or SMA is applied to smooth out transitions: SMA smoothes over the selected length period but adds lag, whereas EMA smoothes amplitude without any additional lag. Hence, to know if the correlation is true or not, try to look at the amplitude and the number of consecutive days the correlation is maintained (both quantities are related), because when the correlation is spurious, it will tend to switch more or less alternatively between 1 and -1 and hence will hover around 0, whereas if the correlation is true, it will get further away from 0 and closer to 1 or -1.
In addition, since there is some time lag for the correlation to switch sign, the area is colored to know the current candle's correlation, regardless of past data's correlation: blue is a positive correlation (1), yellow is negative. The coloring can allow to know a trend reversal early on, but it's noisy.
Finally, symbols with closing days are better accounted for, with the correlation set to 0 on closed days (e.g., on week-ends), and the area is then colored in gray to signal that there is no new correlation data.
This is an improved fork over the original indicator by alexjvale, please show him some love if you like this work:
CFB-Adaptive Trend Cipher Candles [Loxx]CFB-Adaptive Trend Cipher Candles is a candle coloring indicator that shows both trend and trend exhaustion using Composite Fractal Behavior price trend analysis. To do this, we first calculate the dynamic period outputs from the CFB algorithm and then we injection those period inputs into a correlation function that correlates price input price to the candle index. The closer the correlation is to 1, the lighter the green color until the color turns yellow, sometimes, indicating upward price exhaustion. The closer the correlation is to -1, the lighter the red color until it reaches Fuchsia color indicating downward price exhaustion. Green means uptrend, red means downtrend, yellow means reversal from uptrend to downtrend, fuchsia means reversal from downtrend to uptrend.
What is Composite Fractal Behavior ( CFB )?
All around you mechanisms adjust themselves to their environment. From simple thermostats that react to air temperature to computer chips in modern cars that respond to changes in engine temperature, r.p.m.'s, torque, and throttle position. It was only a matter of time before fast desktop computers applied the mathematics of self-adjustment to systems that trade the financial markets.
Unlike basic systems with fixed formulas, an adaptive system adjusts its own equations. For example, start with a basic channel breakout system that uses the highest closing price of the last N bars as a threshold for detecting breakouts on the up side. An adaptive and improved version of this system would adjust N according to market conditions, such as momentum, price volatility or acceleration.
Since many systems are based directly or indirectly on cycles, another useful measure of market condition is the periodic length of a price chart's dominant cycle, (DC), that cycle with the greatest influence on price action.
The utility of this new DC measure was noted by author Murray Ruggiero in the January '96 issue of Futures Magazine. In it. Mr. Ruggiero used it to adaptive adjust the value of N in a channel breakout system. He then simulated trading 15 years of D-Mark futures in order to compare its performance to a similar system that had a fixed optimal value of N. The adaptive version produced 20% more profit!
This DC index utilized the popular MESA algorithm (a formulation by John Ehlers adapted from Burg's maximum entropy algorithm, MEM). Unfortunately, the DC approach is problematic when the market has no real dominant cycle momentum, because the mathematics will produce a value whether or not one actually exists! Therefore, we developed a proprietary indicator that does not presuppose the presence of market cycles. It's called CFB (Composite Fractal Behavior) and it works well whether or not the market is cyclic.
CFB examines price action for a particular fractal pattern, categorizes them by size, and then outputs a composite fractal size index. This index is smooth, timely and accurate
Essentially, CFB reveals the length of the market's trending action time frame. Long trending activity produces a large CFB index and short choppy action produces a small index value. Investors have found many applications for CFB which involve scaling other existing technical indicators adaptively, on a bar-to-bar basis.
Included
Loxx's Expanded Source Types
Related indicators:
Adaptive Trend Cipher loxx]
Dynamic Zones Polychromatic Momentum Candles
RSI Precision Trend Candles
energies_correlation_zscoreA table to help track correlations between the four major energies contracts of the CME. The table shows the z-score of the current correlation value between HO, RB, CL, and NG. The inputs are:
- timeframe: the timeframe of the calcluation. the default is 5 minutes.
- window: the rolling window over which to calculate the correlations. the default is 48, or four hours given the default timeframe.
A score of zer means that the correlation over the latest window is in line with the average for all windows sampled from the chart history. More positive scores imply higher positive correlation than normal, and vice versa for negative scores.
