Change‐Point Detection in the Conditional Correlation Structure of Multivariate Volatility Models

ABSTRACT

We propose semiparametric CUSUM tests to detect a change-point in the correlation structures of nonlinear multivariate models with dynamically evolving volatilities. The asymptotic distributions of the proposed statistics are derived under mild conditions. We discuss the applicability of our method to the most often used models, including constant conditional correlation (CCC), dynamic conditional correlation (DCC), BEKK, corrected DCC, and factor models. Our simulations show that, our tests have good size and power properties. Also, even though the near-unit root property distorts the size and power of tests, de-volatizing the data by means of appropriate multivariate volatility models can correct such distortions. We apply the semiparametric CUSUM tests in the attempt to date the occurrence of financial contagion from the US to emerging markets worldwide during the great recession. Supplementary materials for this article are available online.

KEY WORDS:

• Change-point detection
• Contagion effect
• Monte Carlo simulation
• Time varying correlation structure
• Volatility processes.

SUPPLEMENTARY MATERIALS

The supplemental appendix contains the verifications of the conditions of the main theorem for our examples, additional examples, and further Monte Carlo simulations.

ACKNOWLEDGMENTS

The authors are grateful to Professors Christian Francq and Jean–Michel Zakoian for their comments on the first version of this article and for useful references. The authors also thank the editor, Todd Clark, the associate editor, and two anonymous referees, whose detailed and constructive comments helped to improve the quality of the article.