ℤ-Valued Smooth Transition GARCH Models: Specification and Testing

• 成果类型: Article; Early Access
• 署名作者: Zhu, Fukang; Xu, Nuo; Li, Qi; Ling, Shiqing
• 署名单位: Jilin University; Changchun Normal University; Hong Kong University of Science & Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2637673
• 发表日期: 2026-05-19
• 关键词: Diagnostic checking test; Discrete-valued model; GARCH MODEL; Goodness-of-fit test; Linearity test; inference

摘要

This article introduces a new class of nonlinear models known as the Z-valued smooth transition GARCH model, designed to accommodate Z-valued time series that display asymmetric, nonlinear and highly persistent volatility. The article outlines the maximum likelihood estimation procedure and establishes its consistency and asymptotic normality of the estimated parameters. Three types of tests are studied, including sup-type linearity test, score-based goodness-of-fit test, and residual-based mixed portmanteau diagnostic checking test. The asymptotic properties of these three test statistics are established. To address the computationally complex problems of estimation, the parameterization of the smooth transition function and the optimization algorithm for the estimation procedure in numerical simulations are discussed. The effectiveness of the tests is demonstrated through numerical simulations, and crime and exchange rate datasets are analyzed to showcase the superior performance of the proposed model. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.