An Updated Literature Review of Distance Correlation and its Applications to Time Series

TL;DR

This paper reviews the development and application of distance correlation in time series analysis, highlighting its ability to detect nonlinear dependencies and test for independence.

Contribution

It provides an updated overview of distance correlation methods and demonstrates their effectiveness in identifying nonlinear relationships in time series data.

Findings

Auto-distance correlation detects nonlinear relationships.

Distance correlation can test the i.i.d. hypothesis.

Compared with other dependence measures.

Abstract

The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its applicability to time series analysis. We will see that the auto-distance covariance/correlation function is able to identify nonlinear relationships and can be employed for testing the i.i.d.\ hypothesis. Comparisons with other measures of dependence are included.