Empirical spectral processes and their applications to time series analysis
type: Item
instance of: scholarly article
title: Empirical spectral processes and their applications to time series analysis
zbMATH Open document ID: 0655.60033
DOI: 10.1016/0304-4149(88)90076-2
author: R. Dahlhaus
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: Let X(t) be an r-dimensional strictly stationary Gaussian time series with a matrix \(F=(F_{ab})\) of spectral distribution functions (SDF's). Let \(F^{(N)}\) be the matrix of empirical SDF's. Let \[ E_ N(g)=(N^{1/2}\int^{\pi}_{- \pi}g_{ab}(\lambda)\{dF_{ab}^{(N)}(\lambda)- dF_{ab}(\lambda)\})_{a,b=1,...,r}. \] The author proves weak convergence and equicontinuity of \(E_ N(g)\) for some classes of functions used as index sets for empirical processes. Some applications of general results to the theory of time series are indicated.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4069935
zbMATH Keywords: strictly stationary Gaussian time series
zbMATH Keywords: weak convergence
zbMATH Keywords: equicontinuity
reviewed by: Jiří Anděl
MaRDI profile type: Publication
full work available at URL: 0304-4149(88)90076-2
OpenAlex ID: W2009051438
cites work: Q3947020
cites work: SPECTRAL ANALYSIS WITH TAPERED DATA
cites work: Q3218973
cites work: Q2963743
cites work: On Estimation of the Spectral Function of a Stationary Gaussian Process
cites work: Q3321285
cites work: Convergence of stochastic processes
Wikidata QID: Q127213115
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description: scientific article; zbMATH DE number 4069935