Measuring Nonlinear Dependence in Time Series, a Distance Correlation Approach

We extend the concept of distance correlation of Szekely, Rizzo and Bakirov (The Annals of Statistics, 2007) and propose the auto distance correlation function (ADCF) to measure the temporal dependence structure of time series. Unlike the classic measures of correlations such as the autocorrelation function, the proposed measure is zero if and only if the measured time series components are independent. In this paper, we propose and theoretically verify a subsampling methodology for the inference of sample ADCF for dependent data. Our methodology provides a useful tool for exploring nonlinear dependence structures in time series.