Abstract
The distance covariance function is a new measure of dependence between random vectors. We drop the assumption of iid data to introduce distance covariance for time series. The R package dCovTS provides functions that compute and plot distance covariance and correlation functions for both univariate and multivariate time series. Additionally it includes functions for testing serial independence based on distance covariance. This paper describes the theoretical background of distance covariance methodology in time series and discusses in detail the implementation of these methods with the R package dCovTS.
Highlights
There has been a considerable recent interest in measuring dependence by employing the concept of the distance covariance function
Compared to the classical Pearson autocorrelation function (ACF) which measures the strength of linear dependencies and can be equal to zero even when the variables are related, auto-distance correlation function (ADCF) vanishes only in the case where the observations are independent
The distance correlation plots for both univariate and multivariate time series are obtained by the ADCFplot() and mADCFplot() functions respectively, where the shown critical values are computed by employing bootstrap methodology described in the appropriate section
Summary
There has been a considerable recent interest in measuring dependence by employing the concept of the distance covariance function. Fokianos and Pitsillou (2016b) made this possible by defining the matrix version of pairwise auto-distance covariance and correlation functions They construct multivariate tests of independence based on these new measures in order to identify whether there is some inherent nonlinear interdependence between the component series. The distance correlation plots for both univariate and multivariate time series are obtained by the ADCFplot() and mADCFplot() functions respectively, where the shown critical values (blue dotted horizontal line) are computed by employing bootstrap methodology described in the appropriate section. Recall that these are computed by using the biased definition of distance covariance and correlation. Description Estimates distance correlation for a univariate and multivariate time series respectively Estimates distance covariance for a univariate and multivariate time series respectively Plots sample distance correlation in a univariate and multivariate time series framework respectively Gives a range of univariate kernel function, k(·), that satisfy Assumption 1 Performs a univariate test of independence based on Tn Perform multivariate tests of independence based on Tn and Tn respectively
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