Stochastic Covariance Models

Abstract

A new class of stochastic covariance models based on Wishart distribution is proposed. Three categories of dynamic correlation models are introduced depending on how the time-varying covariance matrix is formulated and whether or not it is a latent variable. A stochastic covariance filter is also developed for filtering and predicting covariances. Extensions of the basic models enable the study of the long memory properties of dynamic correlations, threshold correlation effects and portfolio analysis. Suitable parameterization in the stochastic covariance models and the stochastic covariance filter facilitate efficient calculation of the likelihood function in high-dimensional problems, no matter whether the covariance matrix is observable or latent. Monte Carlo experiments investigating finite sample properties of the maximum likelihood estimator are conducted. Two empirical examples are presented. One deals with the realized covariance of high frequency exchange rate data, while the other examines daily stock returns.

Keywords: Covariance prediction, Dynamic correlation, Nonlinear time series, Long memory, Stochastic covariance filter, Threshold models