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

Yves F. Atchadé, Matias D. Cattaneo

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6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)646-677
Number of pages32
JournalStochastic Processes and their Applications
Issue number1
StatePublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


  • Carlo
  • Central limit theorems
  • Markov chain
  • Markov chains
  • Martingale approximations
  • Monte
  • Quadratic forms
  • U-statistics


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