Break detection in the covariance structure of multivariate time series models

TL;DR

This paper presents a flexible, nonparametric asymptotic test for detecting changes in the covariance structure of multivariate time series, applicable to high-dimensional data and various GARCH models.

Contribution

It introduces a novel asymptotic testing procedure for covariance stability that is nonparametric, broadly applicable, and suitable for high-dimensional multivariate time series.

Findings

Test effectively detects covariance changes in simulations

Applicable to many multivariate GARCH models

Demonstrated usefulness with financial data analysis

Abstract

In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric model selection, model fitting and parameter estimation. We provide the theoretical foundation for the test and demonstrate its applicability via a simulation study and an analysis of financial data. Extensions to multiple changes and the case of infinite fourth moments are also discussed.