Multi-variate stochastic volatility modelling using Wishart autoregressive processes

A new multi-variate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressive parameters and the second step is the unconditional inference, based on a Newton-Raphson iterative algorithm. The proposed methodology, which is mostly Bayesian, is suitable for medium dimensional data and it bridges the gap between closed-form estimation and simulation-based estimation algorithms. An example, consisting of foreign exchange rates data, illustrates the proposed methodology.