Forecasting with VAR models: Fat tails and stochastic volatility

Abstract

We provide evidence that modelling both fat tails and stochastic volatility are important in improving in-sample fit and out-of-sample forecasting performance. To show this, we construct a VAR model where the orthogonalised shocks feature Student’s t distribution as well as time-varying variance. We estimate the model using US data on industrial production growth, inflation, interest rates and stock returns. In terms of in-sample fit, the VAR model featuring both stochastic volatility and t-distributed disturbances outperforms restricted alternatives that feature either attributes. The VAR model with t disturbances results in density forecasts for industrial production and stock returns that are superior to alternatives that assume Gaussianity, and this difference is 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.