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On the spectrum of correlation autoregressive sequences

Author

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  • Makagon, A.
  • Miamee, A. G.

Abstract

In this paper some properties of the correlation autoregressive (CAR) sequences are studied. A representation for the correlation function of an arbitrary CAR sequence is obtained and the relationship between a CAR equation and the growth of the variance and location of spectral lines is revealed. It is also observed that bounded correlation autoregressive sequences coincide with almost periodically correlated sequences with the spectral measure supported on finitely many lines. As a consequence a characterization of the spectrum of a bounded CAR sequence is provided.

Suggested Citation

  • Makagon, A. & Miamee, A. G., 1997. "On the spectrum of correlation autoregressive sequences," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 179-193, September.
    • Handle: RePEc:eee:spapps:v:69:y:1997:i:2:p:179-193
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    References listed on IDEAS

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    1. Hurd Harry L. & Leskow Jacek, 1992. "Strongly Consistent And Asymptotically Normal Estimation Of The Covariance For Almost Periodically Correlated Processes," Statistics & Risk Modeling, De Gruyter, vol. 10(3), pages 201-226, March.
    2. Hurd, Harry L., 1991. "Correlation theory of almost periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 24-45, April.
    3. Léskow, Jacek, 1994. "Asymptotic normality of the spectral density estimators for almost periodically correlated stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 351-360, August.
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