Spectral analysis with replicated time series |
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Authors: | P. Saavedra CN. Hernandez J. Artiles |
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Affiliation: | Department of Mathematics , University of Las Palmas de Gran Canada , Las Palmas de Gran Canaria, Canary Islands, 35017, Spain |
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Abstract: | A doubly stochastic process {x(b,t);b?B,t?Z} is considered, with (B,β,Pβ) being a probability space so that for each b, {X(b,t);t ? Z} is a stationary process with an absolutely continuous spectral distribution. The population spectrum is defined as f(ω) = EB[Q(b,ω)] with Q(b,ω) being the spectral density function of X(b,t). The aim of this paper is to estimate f(ω) by means of a random sample b1,…,br from (B,β,Pβ). For each b1? B, the processes X(b1,t) are observed at the same times t=1,…,N. Thus, r time series (x(b1,t)} are available in order to estimate f(ω). A model for each individual periodogram, which involves f(ω), is formulated. It has been proven that a certain family of linear stationary processes follows the above model In this context, a kernel estimator is proposed in order to estimate f(ω). The bias, variance and asymptotic distribution of this estimator are investigated under certain conditions. |
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Keywords: | average periodogram kernel spectral estimate bandwidth |
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