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.
"Generalized threshold latent variable model." Electron. J. Statist. 13 (1) 2043 - 2092, 2019. https://doi.org/10.1214/19-EJS1571