Forecasting with VAR Models: Fat Tails and Stochastic Volatility

In this paper, we provide evidence that fat tails and stochastic volatility can be important in improving in-sample fit and out-of-sample forecasting performance. Specifically, we construct a VAR model where the orthogonalised shocks feature Student’s t distribution and time-varying variance. We estimate this model using US data on output growth, inflation, interest rates and stock returns. In terms of in-sample fit, the VAR model that features both stochastic volatility and Student’s t-distributed disturbances outperforms restricted alternatives that feature either attributes. The VAR model with Student’s t disturbances results in density forecasts for industrial production and stock returns that are superior to alternatives that assume Gaussianity, and this difference appears to be especially stark over the recent Great Recession. Further international evidence confirms that accounting for both stochastic volatility and Student’s t-distributed disturbances may lead to improved forecast accuracy.