  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 performance and model comparison is done via the
likelihood 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 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 shares and of foreign exchange (FX) rates for 8 currencies, illustrate
the methods. For the IBM data we discuss model performance and multi-step
forecasting in some detail. For the FX data we discuss sequential portfolio
allocation; for both data sets our empirical findings suggest that the TV-VAR
models outperform the widely used VAR models.
