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Estimation of the Fourier coefficient functions and their spectral densities for \gf-mixing almost periodically correlated processes

Author

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  • Hurd, Harry L.
  • Leskow, Jacek

Abstract

The correlation function of an almost periodically correlated process X(t) has the Fourier series R(t + [tau], t) ~ [Sigma][lambda]k[epsilon][Lambda]a[lambda]k([tau]) exp(i[lambda]kt). If X(t) is \gf-mixing, we show for any known [lambda]k that the natural estimator for a[lambda]k([tau]) and the kernel estimator for its spectral density g[lambda]k([gamma]) are consistent in quadratic mean.

Suggested Citation

  • Hurd, Harry L. & Leskow, Jacek, 1992. "Estimation of the Fourier coefficient functions and their spectral densities for \gf-mixing almost periodically correlated processes," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 299-306, July.
    • Handle: RePEc:eee:stapro:v:14:y:1992:i:4:p:299-306
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    Citations

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    Cited by:

    1. Anna E. Dudek, 2018. "Block bootstrap for periodic characteristics of periodically correlated time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 87-124, January.
    2. ŁUkasz Lenart & Jacek Leśkow & Rafał Synowiecki, 2008. "Subsampling in testing autocovariance for periodically correlated time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 995-1018, November.
    3. A. Dudek, 2015. "Circular block bootstrap for coefficients of autocovariance function of almost periodically correlated time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 313-335, April.
    4. Dehay, Dominique & Leskow, Jacek, 1996. "Testing stationarity for stock market data," Economics Letters, Elsevier, vol. 50(2), pages 205-212, February.

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