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Continuous‐Time Stochastic Processes with Cyclical Long‐Range Dependence

Author

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  • V.V. Anh
  • V.P. Knopova
  • N.N. Leonenko

Abstract

This paper introduces continuous‐time random processes whose spectral density is unbounded at some non‐zero frequencies. The discretized versions of these processes have asymptotic properties similar to those of discrete‐time Gegenbauer processes. The paper presents some properties of the covariance function and spectral density as well as a theory of statistical estimation of the mean and covariance function of such processes. Some directions for further generalizations of the results are indicated.

Suggested Citation

  • V.V. Anh & V.P. Knopova & N.N. Leonenko, 2004. "Continuous‐Time Stochastic Processes with Cyclical Long‐Range Dependence," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(2), pages 275-296, June.
    • Handle: RePEc:bla:anzsta:v:46:y:2004:i:2:p:275-296
    DOI: 10.1111/j.1467-842X.2004.00329.x
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    Cited by:

    1. Guglielmo Maria Caporale & Juncal Cuñado & Luis A. Gil-Alana, 2013. "Modelling long-run trends and cycles in financial time series data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 405-421, May.
    2. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2017. "Persistence and cycles in the us federal funds rate," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 1-8.

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