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Article Dans Une Revue Stochastic Processes and their Applications Année : 2009

Central Limit Theorems for arrays of decimated linear processes

Résumé

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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Dates et versions

hal-00277643 , version 1 (06-05-2008)

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Citer

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