Quantitative Financial Risk Management: Theory and Practice

CHAPTER 14

Covariance Specification Tests for Multivariate GARCH Models¹

Gregory Koutmos

Charles F. Dolan School of Business, Fairfield University

INTRODUCTION

Proper modeling of the variances and covariances of financial assets is extremely important for many reasons. For example, risk premia are typically a function of risk that is mostly measured by the variance or the covariance of the asset of interest with some market index. Similarly, risk management requires the use of the variance–covariance matrix of portfolios of risky assets.

Recently, research interest has focused on the time variability of variances and covariances with the use of ARCH-type models. The autoregressive conditionally heteroskedastic model (ARCH) was proposed by Engle (1982) as a way of modeling volatility clustering. Even though the model was originally applied to UK unemployment data, it has been particularly successful in the modeling of variances of financial time series. There is a plethora of applications of univariate ARCH-type models in the area of finance (see Bollerslev, Chou, and Kroner 1992, for an excellent survey). Bollerslev, Engle, and Wooldridge (1988) introduced and estimated the first multivariate GARCH class of models. Koutmos and Booth (1995) introduced a multivariate exponential GARCH model to study volatility spillovers across major national stock markets.

The class of ARCH-type models has been extremely useful in terms of accommodating various hypotheses as well as stylized facts ...