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

Yunzhe Zhou, Chengchun Shi, Lexin Li and Qiwei Yao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: deep conditional generative learning; high-dimensional time series; hypothesis testing; Markov property; mixture density network (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2023-09-30
New Economics Papers: this item is included in nep-big, nep-cmp and nep-ecm
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Published in Journal of the Royal Statistical Society. Series B: Statistical Methodology, 30, September, 2023, 85(4), pp. 1204 - 1222. ISSN: 1369-7412

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:119352

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