Mixtures of t-distributions for finance and forecasting - Raffaella Giacomini; Andreas Gottschling; Christian Haefke; Halbert White (Institute for Advanced Studies (IHS), 2007)
We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. A feature that makes this family particularly desirable for econometric applications is that it possesses closed-form expressions for its anti-derivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we use a scaled and shifted t-distribution to produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-ofsample, than density forecasts obtained using normal or standard t-distributions. In the second application, we replicate the option-pricing exercise of Abadir and Rockinger (2003) using a mixture of scaled and shifted t-distributions and obtain comparably good results, while gaining analytical tractability.
Keywords: C63; C53; C45; 330; ARMA-GARCH models; neural networks; nonparametric density estimation; forecast accuracy; option pricing; risk neutral density; ARCH-Modell; Neuronale Netze; Prognoseverfahren; Nichtparametrisches Verfahren; Schätztheorie