Electronic Journal of Statistics

Generalized threshold latent variable model

Yuanbo Li, Xunze Zheng, and Chun Yip Yau

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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.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 2043-2092.

Dates
Received: April 2018
First available in Project Euclid: 22 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1561168838

Digital Object Identifier
doi:10.1214/19-EJS1571

Mathematical Reviews number (MathSciNet)
MR3973132

Zentralblatt MATH identifier
07080068

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Compound Poisson process ergodicity genetic algorithm minimum description length principle multiple-threshold piecewise modeling

Rights
Creative Commons Attribution 4.0 International License.

Citation

Li, Yuanbo; Zheng, Xunze; Yau, Chun Yip. Generalized threshold latent variable model. Electron. J. Statist. 13 (2019), no. 1, 2043--2092. doi:10.1214/19-EJS1571. https://projecteuclid.org/euclid.ejs/1561168838


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