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Representation of strongly harmonizable periodically correlated processes and their covariances

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  • Hurd, H. L.

Abstract

This paper addresses the representation of continuous-time strongly harmonizable periodically correlated processes and their covariance functions. We show that the support of the 2-dimensional spectral measure is constrained to a set of equally spaced lines parallel to the diagonal. Our main result is that any harmonizable periodically correlated process may be represented in quadratic mean as a Fourier series whose coefficients are a family of unique jointly wide sense stationary processes; the corresponding family of cross spectral distribution functions may be simply identified from the two-dimensional spectral measure resulting from the assumption of strong harmonizability.

Suggested Citation

  • Hurd, H. L., 1989. "Representation of strongly harmonizable periodically correlated processes and their covariances," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 53-67, April.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:1:p:53-67
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    Cited by:

    1. Łukasz Lenart & Błażej Mazur, 2016. "On Bayesian Inference for Almost Periodic in Mean Autoregressive Models," FindEcon Chapters: Forecasting Financial Markets and Economic Decision-Making, in: Magdalena Osińska (ed.), Statistical Review, vol. 63, 2016, 3, edition 1, volume 63, chapter 1, pages 255-272, University of Lodz.
    2. Makagon, Andrzej, 2001. "Characterization of the Spectra of Periodically Correlated Processes," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 1-10, July.
    3. Mitra Ghanbarzadeh & Mina Aminghafari, 2016. "A Wavelet Characterization of Continuous-Time Periodically Correlated Processes with Application to Simulation," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 741-762, November.
    4. Łukasz Lenart & Mateusz Pipień, 2015. "Empirical Properties of the Credit and Equity Cycle within Almost Periodically Correlated Stochastic Processes - the Case of Poland, UK and USA," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 7(3), pages 169-186, September.
    5. Averkamp, Roland, 1997. "Conditions for the completeness of the spectral domain of a harmonizable process," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 1-9, December.
    6. Qin Shao & Robert Lund, 2004. "Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 359-372, May.
    7. Soltani, A.R. & Shishebor, Z. & Zamani, A., 2010. "Inference on periodograms of infinite dimensional discrete time periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 368-373, February.

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