Title: 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.