Abstract
This chapter deals with multivariate time series methods applied to jointly model and forecast variances and covariances when more than two series are involved. Section 6.1 introduces the importance of multivariate applications in finance, and in particular explaining the problem of parameter proliferation typical of sample-based, model-free approaches. Section 6.2 shows how the simple models presented in Chapter 5, can be extended to forecast also conditional covariances and hence correlations. Section 6.3 focuses on full multivariate extensions of GARCH models and explains how to address the problem of over-parameterization. Section 6.4 gives the details of models that can be specifically used to estimate conditional correlations, in particular dynamic conditional correlation models and the associated, restricted case of constant conditional correlation. Section 6.5 explains how factor GARCH model can be constructed and used to avoid excessive parameterizations of multivariate models. Section 6.6 concludes by describing how to estimate the parameters using (Quasi) Maximum Likelihood methods.
Keywords: Correlation forecasting; multivariate covariance models; DCC; CCC; factor GARCH; Vec multivariate GARCH
Essentials of Time Series for Financial Applications 