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Central Limit Theorems for arrays of decimated linear processes

Abstract : Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the spectral density at specific frequencies. Another application, treated elsewhere, concerns the estimation of the long-memory parameter in time-series, using wavelets.
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Submitted on : Tuesday, May 6, 2008 - 7:21:46 PM
Last modification on : Monday, October 19, 2020 - 9:49:26 AM
Long-term archiving on: : Friday, May 28, 2010 - 6:37:20 PM

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François Roueff, Murad Taqqu. Central Limit Theorems for arrays of decimated linear processes. Stochastic Processes and their Applications, Elsevier, 2009, 119 (9), pp.3006-3041. ⟨10.1016/j.spa.2009.03.009⟩. ⟨hal-00277643⟩

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