We confirm that standard time-series models for US output growth, inflation, interest rates and stock market returns feature non-Gaussian error structure. We build a 4-variable VAR model where the orthogonolised shocks have a Student t-distribution with a time-varying variance. We find that in terms of in-sample fit, the VAR model that features both stochastic volatility and Student-t disturbances outperforms restricted alternatives that feature either attributes. The VAR model with Student-t disturbances results in density forecasts for industrial production and stock returns that are superior to alternatives that assume Gaussianity. This difference appears to be especially stark over the recent financial crisis.