Statistica Sinica 13(2003), 1097-1118

TIME SERIES MODELING VIA HIERARCHICAL

MIXTURES

Gabriel Huerta$^1$, Wenxin Jiang$^2$ and Martin A. Tanner$^2$

$^1$University of New Mexico and $^2$Northwestern University

Abstract: We address the problem of model comparison and model mixing in time series using the approach known as Hierarchical Mixtures-of-Experts. Our methodology allows for comparisons of arbitrary models, not restricted to a particular class or parametric form. Additionally, the approach is flexible enough to incorporate exogenous information that can be summarized in terms of covariables or simply time, through weighting functions that define the hierarchical mixture. Huerta, Jiang and Tanner (2001) showed how to estimate the parameters of such models using the EM-algorithm. Here we present some theoretical properties of the method in the context of time series modeling. In addition, we consider model estimation using a full Bayesian approach based on Markov Chain Monte Carlo simulation. Methods for model checking and diagnostics for this class of models are presented. Finally, we explore our methodology by analyzing an economic-financial series: the monthly US industrial production index from 1947 to 1993.

Key words and phrases: Covariables, EM-algorithm, hierarchical mixture, Markov Chain Monte Carlo, time series.