Testing for the Markov property in time series via deep conditional generative learning

• 成果类型: Article
• 署名作者: Zhou, Yunzhe; Shi, Chengchun; Li, Lexin; Yao, Qiwei
• 署名单位: University of California System; University of California Berkeley; University of London; London School Economics & Political Science; University of London; London School Economics & Political Science
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad064
• 发表日期: 2023
• 页码: 1204-1222
• 关键词: geometric ergodicity; neural-networks; selection

摘要

The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a nonparametric test for the Markov property in high-dimensional time series via deep conditional generative learning. We also apply the test sequentially to determine the order of the Markov model. We show that the test controls the type-I error asymptotically, and has the power approaching one. Our proposal makes novel contributions in several ways. We utilise and extend state-of-the-art deep generative learning to estimate the conditional density functions, and establish a sharp upper bound on the approximation error of the estimators. We derive a doubly robust test statistic, which employs a nonparametric estimation but achieves a parametric convergence rate. We further adopt sample splitting and cross-fitting to minimise the conditions required to ensure the consistency of the test. We demonstrate the efficacy of the test through both simulations and the three data applications.