Testing for the Markov Property in Time Series via Deep Conditional Generative Learning
This provides a method for statisticians and data analysts to verify Markov assumptions in time series, which is incremental but addresses a known bottleneck with improved theoretical guarantees.
The authors tackled the problem of testing the Markov property in high-dimensional time series by proposing a nonparametric test using deep conditional generative learning, which asymptotically controls type-I error and has power approaching one, with applications in simulations and three datasets.
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 utilize 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 minimize 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.