Exponential inequalities for nonstationary Markov chains

Alquier Pierre (), Doukhan Paul and Fan Xiequan
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Alquier Pierre: CREST, ENSAE, Université Paris Saclay
Doukhan Paul: AGM UMR8088 UniversityParis-Seine and CIMFAV, Universidad de Valparaiso, Chile
Fan Xiequan: CAM, Tianjin University, Tianjin, China

Dependence Modeling, 2019, vol. 7, issue 1, 150-168

Abstract: Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on inequalities and learning theory for time series, in the past 15 years. However, for the non independent case, almost all the results concern stationary time series. This excludes many important applications: for example any series with a periodic behaviour is nonstationary. In this paper, we extend the basic tools of [19] to nonstationary Markov chains. As an application, we provide a Bernsteintype inequality, and we deduce risk bounds for the prediction of periodic autoregressive processes with an unknown period.

Keywords: Nonstationary Markov chains; Martingales; Exponential inequalities; Time series forecasting; Statistical learning theory; Oracle inequalities; Model selection (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:7:y:2019:i:1:p:150-168:n:7

DOI: 10.1515/demo-2019-0007

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