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Subsampling in testing autocovariance for periodically correlated time series

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  • ŁUkasz Lenart
  • Jacek Leśkow
  • Rafał Synowiecki

Abstract

. The main purpose of this article was to describe the asymptotic properties of subsampling procedure applied to nonstationary, periodically correlated time series. We present the conditions under which the subsampling version for the estimator of Fourier coefficient of autocovariance function is consistent. Our result provides new tools in statistical inference methods for nonstationary, periodically correlated time series. For example, it enables to construct consistent subsampling test which successfully distinguishes the period of the series.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:6:p:995-1018
    DOI: 10.1111/j.1467-9892.2008.00591.x
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    References listed on IDEAS

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    1. Hurd, Harry L., 1991. "Correlation theory of almost periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 24-45, April.
    2. Broszkiewicz-Suwaj, E & Makagon, A & Weron, R & Wyłomańska, A, 2004. "On detecting and modeling periodic correlation in financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 196-205.
    3. 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.
    4. repec:bla:jtsera:v:25:y:2004:3:p:359-372 is not listed on IDEAS
    5. Donald W.K. Andrews, 1983. "First Order Autoregressive Processes and Strong Mixing," Cowles Foundation Discussion Papers 664, Cowles Foundation for Research in Economics, Yale University.
    6. Dehay, Dominique & Leskow, Jacek, 1996. "Testing stationarity for stock market data," Economics Letters, Elsevier, vol. 50(2), pages 205-212, February.
    7. 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.
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    Cited by:

    1. Łukasz Lenart & Mateusz Pipień, 2017. "Non-Parametric Test for the Existence of the Common Deterministic Cycle: The Case of the Selected European Countries," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(3), pages 201-241, September.
    2. Łukasz Lenart, 2016. "Generalized Resampling Scheme With Application to Spectral Density Matrix in Almost Periodically Correlated Class of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 369-404, May.
    3. Lenart, Łukasz, 2013. "Non-parametric frequency identification and estimation in mean function for almost periodically correlated time series," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 252-269.
    4. Łukasz Lenart, 2017. "Examination of Seasonal Volatility in HICP for Baltic Region Countries: Non-Parametric Test versus Forecasting Experiment," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(1), pages 29-67, March.
    5. Dudek, Anna E. & Lenart, Łukasz, 2017. "Subsampling for nonstationary time series with non-zero mean function," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 252-259.
    6. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Dominique Dehay & Anna E. Dudek, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 327-351, May.

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