Central limit theorems for arrays of decimated linear processes

Date Issued
2009-09-01Publisher Version
10.1016/j.spa.2009.03.009Author(s)
Roueff, F.
Taqqu, Murad S.
Metadata
Show full item recordPermanent Link
https://hdl.handle.net/2144/37413Version
First author draft
Citation (published version)
F. Roueff, M.S. Taqqu. 2009. "Central limit theorems for arrays of decimated linear processes." STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Volume 119, Issue 9, pp. 3006 - 3041 (36). https://doi.org/10.1016/j.spa.2009.03.009Abstract
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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