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On the asymptotic distribution of the periodograms for the discrete time harmonizable simple processes

Author

Listed:
  • A. R. Soltani

    (Shiraz University
    College of Science, Kuwait University)

  • A. R. Nematollahi

    (Shiraz University)

  • M. R. Mahmoudi

    (Fasa University)

Abstract

Simple harmonizable processes, introduced by Soltani and Parvardeh (Theory Probab Appl 50(3):448–462, 2006), form a fairly large class of second order processes that includes stationary processes and periodically correlated processes. The spectral density of a simple process is supported by certain curves in $$[0,2\pi )^2$$ [ 0 , 2 π ) 2 . In this article we proceed to the inference for the spectral density of simple processes, including estimation of the spectral density supporting curves and derivation of the asymptotic distribution of the periodogram. We also introduce the “spectral cipher” that highlights active frequencies of a given time series. Theoretical derivations are exhibited using real and simulated data.

Suggested Citation

  • A. R. Soltani & A. R. Nematollahi & M. R. Mahmoudi, 2019. "On the asymptotic distribution of the periodograms for the discrete time harmonizable simple processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 307-322, July.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:2:d:10.1007_s11203-018-9189-5
    DOI: 10.1007/s11203-018-9189-5
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    References listed on IDEAS

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    1. Harry L. Hurd & Neil L. Gerr, 1991. "Graphical Methods For Determining The Presence Of Periodic Correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(4), pages 337-350, July.
    2. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    3. Shishebor, Z. & Soltani, A.R. & Zamani, A., 2011. "Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1118-1125, August.
    4. Vinod, Hrishikesh D. & Lopez-de-Lacalle, Javier, 2009. "Maximum Entropy Bootstrap for Time Series: The meboot R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i05).
    5. A. R. Soltani & M. Azimmohseni, 2007. "Simulation of Real‐Valued Discrete‐Time Periodically Correlated Gaussian Processes with Prescribed Spectral Density Matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 225-240, March.
    6. Pourahmadi, Mohsen & Daniels, Michael J. & Park, Trevor, 2007. "Simultaneous modelling of the Cholesky decomposition of several covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 568-587, March.
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