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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.

Multi‐variate stochastic volatility modelling using Wishart autoregressive processes