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Measuring nonlinear dependence in time‐series, a distance correlation approach
Author(s) -
Zhou Zhou
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00780.x
Subject(s) - autocorrelation , series (stratigraphy) , distance correlation , mathematics , measure (data warehouse) , nonlinear system , correlation , inference , time series , function (biology) , algorithm , statistics , statistical physics , pattern recognition (psychology) , data mining , artificial intelligence , computer science , random variable , paleontology , physics , geometry , quantum mechanics , evolutionary biology , biology
We extend the concept of distance correlation of Szekely et al. (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 article, 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.