Generalized threshold latent variable model

Abstract

This article proposes a generalized threshold latent variable model for flexible threshold modeling of time series. The proposed model encompasses several existing models, and allows a discrete valued threshold variable. Sufficient conditions for stationarity and ergodicity are investigated. The minimum description length principle is applied to formulate a criterion function for parameter estimation and model selection. A computationally efficient procedure for optimizing the criterion function is developed based on a genetic algorithm. Consistency and weak convergence of the parameter estimates are established. Moreover, simulation studies and an application for initial public offering data are presented to illustrate the proposed methodology.