Statistics Seminar: STA 290
Thursday, February 9th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)
Speaker: Daniel Vogel (Technische Universität Dortmund, Germany)
Title: An efficient and robust test for change-point in correlation
Abstract: We propose an asymptotic change-point test for correlation based on Kendall's tau. Suppose we observe a bivariate time series ((Xi; Yi))i=1, . . . , n. The null hypothesis is that Kendall's rank correlation between Xi and Yi stays constant for all i = 1, . . . , n. We assume ((Xi; Yi))i=1, . . . , n to be stationary and near epoch dependent on an absolutely regular process. This large class of processes includes all common time series models as well as many chaotic dynamical systems. In the derivation of the asymptotic distribution of the test statistic, the U-statistic representation of Kendall's tau is employed. Kendall's tau correlation coefficient possesses a high efficiency at the normal distribution, as compared to the normal MLE, Pearson's correlation measure. But contrary to Pearson's correlation coefficient it has excellent robustness properties and shows no loss in efficiency at heavy-tailed distributions. The combination of efficiency and robustness is the advantage of our test over previous proposals of tests for constant correlation. Furthermore, the asymptotic variance of Kendalls tau has a tractable analytic form (in contrast to Spearmans rho for instance). We use a general type of near epoch dependence, which we call P-near epoch dependence (P NED). Contrary to the usually considered Lp, p ≥ 1, near epoch dependence, our formulation does not require the existence of any moments, but includes all Lp NED processes, and is therefore very well suited for our objective: to devise a change-point test for arbitrarily heavy-tailed data.
Co-Authors: Herold Dehling, Martin Wendler, Dominik Wied