calc_covar: Calculate the covariance matrix of the columns of a _time...

In algoquant/HighFreq: High Frequency Time Series Management

Calculate the covariance matrix of the columns of a time series using RcppArmadillo.

Description

Calculate the covariance matrix of the columns of a time series using RcppArmadillo.

Usage

calc_covar(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 covariance 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_covar() calculates the covariance matrix of the columns of a time series or a matrix of data using RcppArmadillo C++ code. The covariance is a measure of the codependency of the data.

If method = "moment" (the default) then calc_covar() calculates the covariance as the second co-moment:

\sigma_{xy} = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x}) (y_i - \bar{y})

Then calc_covar() performs the same calculation as the R function stats::cov().

If method = "quantile" then it calculates the covariance as the difference between the quantiles as follows:

\mu = q_{\alpha} - q_{1-\alpha}

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

If method = "nonparametric" then it calculates the covariance as the Median Absolute Deviation (MAD):

MAD = median(abs(x - median(x)))

It also multiplies the MAD by a factor of 1.4826, to make it comparable to the standard deviation.

If method = "nonparametric" then calc_covar() performs the same calculation as the function stats::mad(), but it's much faster because it uses RcppArmadillo C++ code.

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

Value

A square matrix with the covariance coefficients of the columns of the time series tseries.

Examples

## Not run: 
# Calculate VTI and XLF returns
retp <- na.omit(rutils::etfenv$returns[, c("VTI", "XLF")])
# Compare HighFreq::calc_covar() with standard var()
all.equal(drop(HighFreq::calc_covar(retp)), 
  cov(retp), check.attributes=FALSE)
# Compare the speed of RcppArmadillo with matrixStats and with R code
library(microbenchmark)
summary(microbenchmark(
  Rcpp=HighFreq::calc_covar(retp),
  Rcode=cov(retp),
  times=10))[, c(1, 4, 5)]  # end microbenchmark summary
# Compare HighFreq::calc_covar() with stats::mad()
all.equal(drop(HighFreq::calc_covar(retp, method="nonparametric")), 
  sapply(retp, mad), check.attributes=FALSE)
# Compare the speed of RcppArmadillo with stats::mad()
summary(microbenchmark(
  Rcpp=HighFreq::calc_covar(retp, method="nonparametric"),
  Rcode=sapply(retp, mad),
  times=10))[, c(1, 4, 5)]  # end microbenchmark summary

## End(Not run)

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