B1729
Title: Change-point tests and estimators for gradually changing dependence structures based on Kendalls tau
Authors: Jean-Francois Quessy - Universite Du Quebec a Trois-Rivieres (Canada)
Felix Camirand Lemyre - Université de Sherbrooke (Canada) [presenting]
Abstract: Suppose that pairs $(X_1, Y_1),\ldots, (X_n, Y_n)$ of independent observations are subject to a gradual change in their stochastic behaviour in the sense that for given $K_1 < K_2$, between 1 and $n$, the underlying joint distribution of a given pair is $F$ before $K_1$, $G$ after $K_2 > K_1$, and gradually moving from $F$ to $G$ between the two times of change $K_1$ and $K_2$. This setup elegantly generalizes the usual abrupt change model, which is usually assumed in the change-point analysis. Under this configuration, asymptotically unbiased estimators of Kendall's tau up to the change and after the change are derived, as well as tests and estimators of gradual change points related to these measures of association. The asymptotic behaviour of the introduced estimators and test statistics as n goes to infinity is rigorously investigated, in particular by demonstrating a general result (of independent interest) concerning weighted indexed U-statistics computed under heterogeneous data. The sampling properties of the proposed estimators of the Kendall taus, tests for change-point detection and estimator of times of change are studied in a simulation study that considers various scenarios of gradual changes in dependence. The usefulness of the introduced tools is illustrated on a multivariate time series of monthly consumer price index in the United States.