Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/52420
Title: Spectral analysis with replicated time series
Authors: Saavedra Santana, Pedro 
Hernández, C. N. 
Artiles, J. 
UNESCO Clasification: 240401 Bioestadística
Keywords: Average periodogram
Kernel spectral estimate
Bandwidth
Issue Date: 2000
Journal: Communications in Statistics - Theory and Methods 
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.
URI: http://hdl.handle.net/10553/52420
ISSN: 0361-0926
DOI: 10.1080/03610920008832610
Source: Communications in Statistics - Theory and Methods [ISSN 0361-0926], v. 29 (11), p. 2343-2362
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