calc_kurtosis: Calculate the kurtosis of the columns of a _time series_ or a...

In algoquant/HighFreq: High Frequency Time Series Management

Calculate the kurtosis of the columns of a time series or a matrix using RcppArmadillo.

Description

Calculate the kurtosis of the columns of a time series or a matrix using RcppArmadillo.

Usage

calc_kurtosis(tseries, method = "moment", confl = 0.75)

Arguments

tseries	A time series or a matrix of data.
method	A character string specifying the type of the kurtosis model (the default is method = "moment" - see Details).
confl	The confidence level for calculating the quantiles of returns (the default is confl = 0.75).

Details

The function calc_kurtosis() calculates the kurtosis of the columns of the matrix tseries using RcppArmadillo C++ code.

If method = "moment" (the default) then calc_kurtosis() calculates the fourth moment of the data. But it doesn't center the columns of tseries because that requires copying the matrix tseries in memory, so it's time-consuming.

If method = "quantile" then it calculates the skewness \kappa from the differences between the quantiles of the data as follows:

\kappa = \frac{q_{\alpha} - q_{1-\alpha}}{q_{0.75} - q_{0.25}}

Where \alpha is the confidence level for calculating the quantiles.

If method = "nonparametric" then it calculates the kurtosis as the difference between the mean of the data minus its median, divided by the standard deviation.

If the number of rows of tseries is less than 3 then it returns zeros.

The code examples below compare the function calc_kurtosis() with the kurtosis calculated using R code.

Value

A single-row matrix with the kurtosis of the columns of tseries.

Examples

## Not run: 
# Define a single-column time series of returns
retp <- na.omit(rutils::etfenv$returns$VTI)
# Calculate the moment kurtosis
HighFreq::calc_kurtosis(retp)
# Calculate the moment kurtosis in R
calc_kurtr <- function(x) {
  x <- (x-mean(x))
  sum(x^4)/var(x)^2/NROW(x)
}  # end calc_kurtr
all.equal(HighFreq::calc_kurtosis(retp), 
  calc_kurtr(retp), check.attributes=FALSE)
# Compare the speed of RcppArmadillo with R code
library(microbenchmark)
summary(microbenchmark(
  Rcpp=HighFreq::calc_kurtosis(retp),
  Rcode=calc_kurtr(retp),
  times=10))[, c(1, 4, 5)]  # end microbenchmark summary
# Calculate the quantile kurtosis
HighFreq::calc_kurtosis(retp, method="quantile", confl=0.9)
# Calculate the quantile kurtosis in R
calc_kurtq <- function(x, a=0.9) {
  	quantiles <- quantile(x, c(1-a, 0.25, 0.75, a), type=5)
  	(quantiles[4] - quantiles[1])/(quantiles[3] - quantiles[2])
}  # end calc_kurtq
all.equal(drop(HighFreq::calc_kurtosis(retp, method="quantile", confl=0.9)), 
  calc_kurtq(retp, a=0.9), check.attributes=FALSE)
# Compare the speed of RcppArmadillo with R code
summary(microbenchmark(
  Rcpp=HighFreq::calc_kurtosis(retp, method="quantile"),
  Rcode=calc_kurtq(retp),
  times=10))[, c(1, 4, 5)]  # end microbenchmark summary
# Calculate the nonparametric kurtosis
HighFreq::calc_kurtosis(retp, method="nonparametric")
# Compare HighFreq::calc_kurtosis() with R nonparametric kurtosis
all.equal(drop(HighFreq::calc_kurtosis(retp, method="nonparametric")), 
  (mean(retp)-median(retp))/sd(retp), 
  check.attributes=FALSE)
# Compare the speed of RcppArmadillo with R code
summary(microbenchmark(
  Rcpp=HighFreq::calc_kurtosis(retp, method="nonparametric"),
  Rcode=(mean(retp)-median(retp))/sd(retp),
  times=10))[, c(1, 4, 5)]  # end microbenchmark summary

## End(Not run)

algoquant/HighFreq documentation built on Feb. 9, 2024, 8:15 p.m.