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

Zhou, Yunzhe, Shi, Chengchun ORCID: 0000-0001-7773-2099, Li, Lexin and Yao, Qiwei ORCID: 0000-0003-2065-8486 (2023) Testing for the Markov property in time series via deep conditional generative learning. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 85 (4). 1204 - 1222. ISSN 1369-7412

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Abstract

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.

Item Type:	Article
Official URL:	https://academic.oup.com/jrsssb
Additional Information:	© 2023 The Author
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	06 Jun 2023 15:39
Last Modified:	20 Dec 2024 00:48
URI:	http://eprints.lse.ac.uk/id/eprint/119352

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