Joint and Conditional Transformed T−Mixture Models with Applications to Financial and Economic Data

Abstract

We estimate joint and conditional probability densities via a new hybrid approach that incorporates ideas from copula modeling and makes use of known analytic results involving the conditional distributions of multivariate random variables that have joint (usual) multivariate t or t−mixture distributions. Our method amounts to the application of t or t−mixture modeling in a special “working space” that is used in copula modeling. We also provide new simulation algorithms and describe numerical experiments, performed on accounting data, stock return data, and housing price data, in which we compare the performance of our method with a number of benchmark approaches.

Keywords: Copula, Conditional Probability Density, Gaussian Mixture Model, t−Mixture Model, Multivariate Probability Distribution, Multivariate t−Distribution, Arellano-Valle and Bolfarine’s Generalized t−distribution, Fat-Tailed, Simulation, Stock Return Distribution, Financial Data, Economic Data