Central Limit Theorems for arrays of decimated linear processes

Details Central Limit Theorems for arrays of decimated linear processes Central Limit Theorems for arrays of decimated linear processes

2008-05-06

arxiv.org/abs/0805.0779v1

Mathematics

Statistics Theory

Scientific paper

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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