A martingale decomposition for quadratic forms of Markov chains (with applications)

Yves Atchade and Matias Cattaneo

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 646-677

Abstract: We develop a martingale-based decomposition for a general class of quadratic forms of Markov chains, which resembles the well-known Hoeffding decomposition of U-statistics of i.i.d. data up to a reminder term. To illustrate the applicability of our results, we discuss how this decomposition may be used to studying the large-sample properties of certain statistics in two problems: (i) we examine the asymptotic behavior of lag-window estimators in time series, and (ii) we derive an asymptotic linear representation and limiting distribution of U-statistics with varying kernels in time series. We also discuss simplified examples of interest in statistics and econometrics.

Keywords: Central limit theorems; Markov chains; Markov chain Monte Carlo; Martingale approximations; Quadratic forms; U-statistics (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:1:p:646-677

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DOI: 10.1016/j.spa.2013.09.001

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