A Shift Test for Independence in Generic Time Series

Kenneth D. Harris

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arXiv · 2012.06862

A Shift Test for Independence in Generic Time Series

Kenneth D. Harris

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Abstract

We describe a family of conservative statistical tests for independence of two autocorrelated time series. The series may take values in any sets, and one of them must be stationary. A user-specified function quantifying the association of a segment of the two series is compared to an ensemble obtained by time-shifting the stationary series -N to N steps. If the series are independent, the unshifted value is in the top m shifted values with probability at most m/(N+1). For large N, the probability approaches m/(2N+1). A conservative test rejects independence at significance {\alpha} if the unshifted value is in the top {\alpha}(N+1), and has half the power of an approximate test valid in the large N limit. We illustrate this framework with a test for correlation of autocorrelated categorical time series.

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Kenneth D. Harris. 2020-12-12. A Shift Test for Independence in Generic Time Series. https://arxiv.org/abs/2012.06862

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