Testing for Changes in the Rank Correlation of Time Series

Abstract

Abstract. For a bivariate time series ((Xi, Yi))i=1,...,n we want to detect whether the corre-lation between Xi and Yi stays constant for all i = 1,..., n. We propose a nonparametric change-point test statistic based on Kendall’s tau. The asymptotic distribution under the null hypothesis of no change follows from a new U-statistic invariance principle. Assuming a single change-point, we show that the location of the change-point is consistently estimated. Kendall’s tau possesses a high efficiency at the normal distribution, as compared to the normal maximum likelihood estimator, Pearson’s moment correlation. Contrary to Pearson’s correlation coefficient, it has excellent robustness properties and shows no loss in efficiency at heavy-tailed distributions. The motivation for this research article originates in financial data situations, where heavy tails are common and Kendall’s tau is a more efficient estimator than the moment correlation. We assume the data ((Xi, Yi))i=1,...,n to be stationary and P-near epoch dependent on an absolutely regular process. The P-near epoch dependence condition constitutes a generaliza-tion of the usually considered Lp-near epoch dependence, p ≥ 1, that allows for arbitrarily heavy-tailed data. We investigate the test numerically and compare it to previous proposals. 1.

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