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

Author:

Zhou Yunzhe1,Shi Chengchun2,Li Lexin1ORCID,Yao Qiwei2ORCID

Affiliation:

1. Division of Biostatistics, University of California at Berkeley , Berkeley, CA , USA

2. London School of Economics and Political Science , London , UK

Abstract

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.

Funder

EPSRC

NSF

NIH

Publisher

Oxford University Press (OUP)

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

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