Bayesian dynamic density estimation

Abstract

Empirical distributions in finance and economics might show heavy tails, volatility clustering, varying mean returns and multimodality as part of their features. However, most statistical models available in the literature assume some kind of parametric form (clearly neglecting important characteristics of the data) or focus on modeling extreme events (therefore, providing no information about the rest of the distribution). In this paper we develop a Bayesian nonparametric prior for a collection of distributions evolving in discrete time. The prior is constructed by defining the distribution at any time point as a Dirichlet process mixture of Gaussian distributions, and inducing dependence through the atoms of their stick-breaking decomposition. A general construction, which allows for trends, periodicities and regressors is described. The resulting model is applied to the estimation of the time-varying travel expense distribution of employees from a major development bank comparable to the IDB, IMF and World Bank.