Mixtures of t-distributions for finance and forecasting

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. Particularly desirable for econometric applications are closed-form expressions for antiderivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-of-sample, than density forecasts obtained using normal or standard t-distributions. In the second application, we replicate the option-pricing exercise of Abadir and Rockinger [Density functionals, with an option-pricing application. Econometric Theory 19, 778–811.] and obtain comparably good results, while gaining analytical tractability.