Time-varying vector autoregressive models with stochastic volatility

The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility covariance matrix of the time series is modelled via inverted Wishart and singular multivariate beta distributions allowing a fully conjugate Bayesian inference. Model assessment and model comparison are performed via the log-posterior function, sequential Bayes factors, the mean of squared standardized forecast errors, the mean of absolute forecast errors (known also as mean absolute deviation), and the mean forecast error. Bayes factors are also used in order to choose the autoregressive (AR) order of the model. Multi-step forecasting is discussed in detail and a flexible formula is proposed to approximate the forecast function. Two examples, consisting of bivariate data of IBM and Microsoft shares and of a 30-dimensional asset selection problem, illustrate the methods. For the IBM and Microsoft data we discuss model performance and multi-step forecasting in some detail. For the basket of 30 assets we discuss sequential portfolio allocation; for both data sets our empirical findings suggest that the TV-VAR models outperform the widely used vector AR models.