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SPECTRAL ESTIMATION AND DECONVOLUTION FOR A LINEAR TIME SERIES MODEL
Author(s) -
Pawitan Yudianto,
Shumway R. H.
Publication year - 1989
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1989.tb00019.x
Subject(s) - mathematics , deconvolution , estimator , convolution (computer science) , blind deconvolution , series (stratigraphy) , spectral density estimation , statistics , algorithm , fourier transform , mathematical analysis , computer science , machine learning , artificial neural network , biology , paleontology
. A vector linear time series model is observed as the sum of a convolution of an unknown signal and an additive noise process. The main objective is the estimation or deconvolution of the signal when the spectra of the signal and noise processes are unknown. We prove the strong consistency of a class of nonparametric spectral estimators derived by maximizing a particular Gaussian likelihood function. We also study the mean square convergence of the finite‐sample deconvolution estimators as a function of the sample length T , the filter length M and the spectral bandwidth B T = L T /T .