Logistic Mixtures of Generalized Linear Model Times Series

Abstract

In this dissertation we propose a class of time series models for mixture data. We call these logistic mixtures. In such models the mixture's component densities have a generalized linear model (GLM) form. The regime probabilities are allowed to change over time and are modeled with a logistic regression structure. The regressors of both the component GLM distributions and the logistic probabilities may include covariates as well as past values of the process. We develop an EM algorithm for estimation, give conditions for consistency and asymptotic normality, examine the model through simulations, and apply it to rain rate data. Finally, we consider a likelihood ratio-based test for determining if the data arise from a logistic mixture versus the null hypothesis of the data coming from a single distribution (i.e. no mixture). Because the mixture probabilities are not constant, we are able to develop a test that avoids some of the problems associated with likelihood ratio tests of mixtures.