Representation of strongly harmonizable periodically correlated processes and their covariances
type: Item
instance of: scholarly article
title: Representation of strongly harmonizable periodically correlated processes and their covariances
zbMATH Open document ID: 0689.60039
DOI: 10.1016/0047-259X(89)90076-6
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: This paper discusses the representation of continuous-time strongly harmonizable periodically correlated processes and their covariance functions. It contains several nice results of which two are stated here. 1) It is shown that the 2-dimensional spectral measure of such processes are concentrated on a set of equally spaced lines parallel to the main diagonal. 2) It is proved that any continuous-time strongly harmonizable periodically correlated process with period T may be represented, in quadratic mean as \[ X_ t=\sum_{k}a_ k(t)\exp (i2\pi Kt/T), \] where \(a_ k(t)\), \(-\infty <t<\infty\), \(-\infty <k<\infty\), are stationary and stationary correlated processes with specific covariance and cross covariance functions.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G05
Mathematics Subject Classification ID: 60G12
zbMATH DE Number: 4129742
zbMATH Keywords: representation
zbMATH Keywords: strongly harmonizable periodically correlated processes
zbMATH Keywords: spectral measure
zbMATH Keywords: covariance and cross covariance functions
author: H. L. Hurd
reviewed by: Habib Salehi
MaRDI profile type: Publication
cites work: Q5613639
cites work: Periodically and Almost-Periodically Correlated Random Processes with a Continuous Time Parameter
cites work: Periodically Correlated Processes with Discontinuous Correlation Functions
cites work: Characterization of cyclostationary random signal processes
cites work: Q5585825
cites work: The distribution of the sequential decoding computation time
cites work: Time series with periodic structure
cites work: Q5684728
cites work: Stationarizing Properties of Random Shifts
cites work: Q3332012
cites work: Q3871779
cites work: On periodic and multiple autoregressions
cites work: Q3876877
cites work: Q3843987
cites work: Q4064782
cites work: Q4725402
cites work: Q5807917
cites work: On harmonizable stochastic processes
cites work: Testing for harmonizability
full work available at URL: 0047-259x(89)90076-6
OpenAlex ID: W1999105231
description: scientific article; zbMATH DE number 4129742