Periodically Correlated Solutions to a Class of Stochastic Difference Equations

  • Georgi N. Boshnakov
Part of the Progress in Systems and Control Theory book series (PSCT, volume 23)

Abstract

The class of the periodically correlated processes sets up one of the possible frameworks for description and modeling of time series having pseudo-periodic behaviour. The mean and the autocovariance functions of the processes from this class are periodic. Many of the concepts of the stationary theory admit generalization to the periodic case. There is a duality between the multivariate stationary processes and the periodically correlated processes which makes the investigation of these two classes theoretically equivalent. A survey on these questions (mainly from an algorithmic point of view) and a lot of references may be found in Boshnakov [Bo].

Keywords

Covariance Autocorrelation Crosscorrelation 

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References

  1. [Bo]
    G. N. Boshnakov. Periodically correlated sequences: Some properties and recursions. Research Report 1, Division of Quality Technology and Statistics, Luleo University, Sweden, Mar 1994.Google Scholar
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    P.J. Brockwell and R.A. Davis. Time series: theory and methods Springer Series in Statistics. Springer, second edition, 1991.Google Scholar
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    R.H. Jones and W.M. Brelsford. Time series with periodic structure. Biometrika 54 (1967), 403–408.MathSciNetMATHGoogle Scholar
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    H. Lütkepohl and E.O. Maschke. Bemerkung zur Lösung der YuleWalker-Gleihungen. Metrika, 35/5 (1988), 287–289.CrossRefGoogle Scholar
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    M. Pagano. On periodic and multiple autoregression. Ann. Statist., 6 (1978), 1310–1317.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Georgi N. Boshnakov
    • 1
  1. 1.Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria

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