Detecting changes in cross-sectional dependence in multivariate time series

Abstract

Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes better, a test is introduced based on a recently studied variant of the sequential empirical copula process. In contrast to earlier attempts, ranks are computed with respect to relevant subsamples, with beneficial consequences for the sensitivity of the test. For the computation of p-values we propose a multiplier resampling scheme that takes the serial dependence into account. The large-sample theory for the test statistic and the resampling scheme is developed. The finite-sample performance of the procedure is assessed by Monte Carlo simulations. Two case studies involving time series of financial returns are presented as well.Our test statistic is based on the difference process, D n , defined byFor every s ∈ [0, 1], it gives a weighted difference between the empirical copulas at u of the first ⌊ns⌋ and the last n − ⌊ns⌋ points of the sample. Large absolute differences point in the direction of a change in the copula.To aggregate over u, we consider the Cramér-von Mises statistic S n,k = [0,1] d

Combining Cumulative Sum Change‐Point Detection Tests for Assessing the Stationarity of Univariate Time Series

“…However, preliminary numerical experiments (some of which are reported in Section 5) revealed the low power of such an adaptation in the case of the empirical d.f.‐based tests, especially when the non‐stationarity of the underlying univariate time series is a consequence of changes in the serial dependence. These empirical conclusions, in line with those drawn in Bücher et al () in a related context, prompted us to consider the alternative approach consisting of assessing changes in the ‘contemporary’ distribution (i.e., of the X i ) separately from changes in the serial dependence.…”

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

“…As discussed in Bücher et al [10], a broad class of nonparametric tests for change-point detection particularly sensitive to changes in the copula can be derived from the process…”

“…. , M }, W Additional details, simulation results as well as illustrations on financial data can be found in Bücher et al [10] for tests based on maximally selected Cramér-von Mises statistics.…”

Monitoring Test for Stability of Dependence Structure in Multivariate Data Based on Copula

“…Recently, the problem of testing constancy of the copula has been studied by Quessy et al [13], Bücher and Ruppert [14], and Bücher et al [15]. All of these approaches are devoted to the change point detection within data sets of fixed size.…”