Colloquium Mathematics - Dr. A. Betken

Title: Rank-based change-point tests for long-range dependent time series

Abstract:

Following an introduction to change-point analysis and the concept of longrange dependent time series, we will consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series, the asymptotic distributions of the corresponding test statistics are derived. For this, we consider a uniform reduction principle for the empirical process in a two-parameter Skorohod space equipped with a weighted supremum norm. Moreover, special emphasis is laid on an application-oriented approach to the mathematical results by considering self-normalized statistics and an approximation of the distribution of test statistics by subsampling procedures. Theoretical results are motivated by data and accompanied by simulations.

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