STATISTICS
COLLOQUIUM
Thursday,
February 9th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 4110
(Statistics Lounge)
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
