On Construction and Estimation of Stationary Mixture Transition Distribution Models

• Activity Number: 279 - SBSS Paper Competition Winners
• Type: Topic-Contributed
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xiaotian Zheng* and Athanasios Kottas and Bruno Sansó
• Companies: University of California, Santa Cruz and University of California, Santa Cruz and University of California, Santa Cruz
• Keywords: Bayesian inference; First-order strict stationarity; Markov chain Monte Carlo; Non-Gaussian time series

Abstract

Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary mixture transition distribution models that extend beyond linear, Gaussian dynamics. We study conditions for first-order strict stationarity which allow for different constructions with either continuous or discrete families for the first-order transition densities given a pre-specified family for the marginal density, and with general forms for the resulting conditional expectations. Inference and prediction are developed under the Bayesian framework with particular emphasis on flexible, structured priors for the mixture weights. Model properties are investigated both analytically and through synthetic data examples. Finally, Poisson and Lomax examples are illustrated through real data applications.