  Obtaining reliable estimates of conditional covariance matrices is an
important task of heteroskedastic multivariate time series. In portfolio
optimization and financial risk management, it is crucial to provide measures
of uncertainty and risk as accurately as possible. We propose using mixture
vector autoregressive (MVAR) models for portfolio optimization. Combining a
mixture of distributions that depend on the recent history of the process, MVAR
models can accommodate asymmetry, multimodality, heteroskedasticity and
cross-correlation in multivariate time series data. For mixtures of Normal
components, we exploit a property of the multivariate Normal distribution to
obtain explicit formulas of conditional predictive distributions of returns on
a portfolio of assets. After showing how the method works, we perform a
comparison with other relevant multivariate time series models on real stock
return data.
