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Non-parametric frequency identification and estimation in mean function for almost periodically correlated time series

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  • Lenart, Łukasz

Abstract

The aim of this article is to present a non-parametric way to identify and estimate the unknown frequencies in the Fourier representation of mean function for almost periodically correlated time series. We state the exact form of asymptotic distribution of normalized estimator of Fourier coefficient for fixed frequency in considered class of time series. Next, we prove the consistency of subsampling procedure applied for the Fourier coefficient. Based on these results we propose a graphical method for determining the presence of periodic or almost periodic structure of mean function. Finally, following Walker (1971) [37] we construct a consistent estimator of frequency and corresponding Fourier coefficient.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:252-269
    DOI: 10.1016/j.jmva.2012.10.006
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Lukasz Lenart & Blazej Mazur & Mateusz Pipien, 2016. "Statistical Analysis Of Business Cycle Fluctuations In Poland Before And After The Crisis," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 11(4), pages 769-783, December.
    5. 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.
    6. Lukasz Lenart, 2015. "Discrete Spectral Analysis. The Case of Industrial Production in Selected European Countries," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 15, pages 27-47.
    7. 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.
    8. 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.
    9. Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(2), pages 95-116, June.
    10. 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.

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