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

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.