HurstExponentLibrary "HurstExponent"
Library to calculate Hurst Exponent refactored from Hurst Exponent - Detrended Fluctuation Analysis
demean(src) Calculates a series subtracted from the series mean.
Parameters:
src : The series used to calculate the difference from the mean (e.g. log returns).
Returns: The series subtracted from the series mean
cumsum(src, length) Calculates a cumulated sum from the series.
Parameters:
src : The series used to calculate the cumulative sum (e.g. demeaned log returns).
length : The length used to calculate the cumulative sum (e.g. 100).
Returns: The cumulative sum of the series as an array
aproximateLogScale(scale, length) Calculates an aproximated log scale. Used to save sample size
Parameters:
scale : The scale to aproximate.
length : The length used to aproximate the expected scale.
Returns: The aproximated log scale of the value
rootMeanSum(cumulativeSum, barId, numberOfSegments) Calculates linear trend to determine error between linear trend and cumulative sum
Parameters:
cumulativeSum : The cumulative sum array to regress.
barId : The barId for the slice
numberOfSegments : The total number of segments used for the regression calculation
Returns: The error between linear trend and cumulative sum
averageRootMeanSum(cumulativeSum, barId, length) Calculates the Root Mean Sum Measured for each block (e.g the aproximated log scale)
Parameters:
cumulativeSum : The cumulative sum array to regress and determine the average of.
barId : The barId for the slice
length : The length used for finding the average
Returns: The average root mean sum error of the cumulativeSum
criticalValues(length) Calculates the critical values for a hurst exponent for a given length
Parameters:
length : The length used for finding the average
Returns: The critical value, upper critical value and lower critical value for a hurst exponent
slope(cumulativeSum, length) Calculates the hurst exponent slope measured from root mean sum, scaled to log log plot using linear regression
Parameters:
cumulativeSum : The cumulative sum array to regress and determine the average of.
length : The length used for the hurst exponent sample size
Returns: The slope of the hurst exponent
smooth(src, length) Smooths input using advanced linear regression
Parameters:
src : The series to smooth (e.g. hurst exponent slope)
length : The length used to smooth
Returns: The src smoothed according to the given length
exponent(src, hurstLength) Wrapper function to calculate the hurst exponent slope
Parameters:
src : The series used for returns calculation (e.g. close)
hurstLength : The length used to calculate the hurst exponent (should be greater than 50)
Returns: The src smoothed according to the given length
Moments
MomentsLibrary "Moments"
Based on Moments (Mean,Variance,Skewness,Kurtosis) . Rewritten for Pinescript v5.
logReturns(src) Calculates log returns of a series (e.g log percentage change)
Parameters:
src : Source to use for the returns calculation (e.g. close).
Returns: Log percentage returns of a series
mean(src, length) Calculates the mean of a series using ta.sma
Parameters:
src : Source to use for the mean calculation (e.g. close).
length : Length to use mean calculation (e.g. 14).
Returns: The sma of the source over the length provided.
variance(src, length) Calculates the variance of a series
Parameters:
src : Source to use for the variance calculation (e.g. close).
length : Length to use for the variance calculation (e.g. 14).
Returns: The variance of the source over the length provided.
standardDeviation(src, length) Calculates the standard deviation of a series
Parameters:
src : Source to use for the standard deviation calculation (e.g. close).
length : Length to use for the standard deviation calculation (e.g. 14).
Returns: The standard deviation of the source over the length provided.
skewness(src, length) Calculates the skewness of a series
Parameters:
src : Source to use for the skewness calculation (e.g. close).
length : Length to use for the skewness calculation (e.g. 14).
Returns: The skewness of the source over the length provided.
kurtosis(src, length) Calculates the kurtosis of a series
Parameters:
src : Source to use for the kurtosis calculation (e.g. close).
length : Length to use for the kurtosis calculation (e.g. 14).
Returns: The kurtosis of the source over the length provided.
skewnessStandardError(sampleSize) Estimates the standard error of skewness based on sample size
Parameters:
sampleSize : The number of samples used for calculating standard error.
Returns: The standard error estimate for skewness based on the sample size provided.
kurtosisStandardError(sampleSize) Estimates the standard error of kurtosis based on sample size
Parameters:
sampleSize : The number of samples used for calculating standard error.
Returns: The standard error estimate for kurtosis based on the sample size provided.
skewnessCriticalValue(sampleSize) Estimates the critical value of skewness based on sample size
Parameters:
sampleSize : The number of samples used for calculating critical value.
Returns: The critical value estimate for skewness based on the sample size provided.
kurtosisCriticalValue(sampleSize) Estimates the critical value of kurtosis based on sample size
Parameters:
sampleSize : The number of samples used for calculating critical value.
Returns: The critical value estimate for kurtosis based on the sample size provided.
