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Trimming and Tapering Semi‐Parametric Estimates in Asymmetric Long Memory Time Series

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  • J. Arteche
  • C. Velasco

Abstract

. This paper considers semi‐parametric frequency domain inference for seasonal or cyclical time series with asymmetric long memory properties. It is shown that tapering the data reduces the bias caused by the asymmetry of the spectral density at the cyclical frequency. We provide a joint treatment of different tapering schemes and of the log‐periodogram regression and Gaussian semi‐parametric estimates of the memory parameters. Tapering allows for a less restrictive trimming of frequencies for the analysis of the asymptotic properties of both estimates when allowing for asymmetries. Simple rules for inference are feasible thanks to tapering and their validity in finite samples is investigated in a simulation exercise and for an empirical example.

Suggested Citation

  • J. Arteche & C. Velasco, 2005. "Trimming and Tapering Semi‐Parametric Estimates in Asymmetric Long Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 581-611, July.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:4:p:581-611
    DOI: 10.1111/j.1467-9892.2005.00431.x
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    References listed on IDEAS

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    1. Arteche, Josu & Robinson, Peter M., 1998. "Seasonal and cyclical long memory," LSE Research Online Documents on Economics 2241, London School of Economics and Political Science, LSE Library.
    2. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    3. Javier Hidalgo & Philippe Soulier, 2004. "Estimation of the location and exponent of the spectral singularity of a long memory process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 55-81, January.
    4. Josu Arteche & Peter M. Robinson, 2000. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 1-25, January.
    5. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    6. Yoshihiro Yajima, 1989. "A Central Limit Theorem Of Fourier Transforms Of Strongly Dependent Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(4), pages 375-383, July.
    7. Josu Arteche, 2002. "Semiparametric robust tests on seasonal or cyclical long memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 251-285, May.
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    Cited by:

    1. Artiach, Miguel & Arteche, Josu, 2012. "Doubly fractional models for dynamic heteroscedastic cycles," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2139-2158.
    2. Reisen, Valdério A. & Zamprogno, Bartolomeu & Palma, Wilfredo & Arteche, Josu, 2014. "A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 98(C), pages 1-17.
    3. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    4. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    5. Yuliya Lovcha & Alejandro Perez-Laborda & Luis Gil-Alana, 2018. "On the invertibility of seasonally adjusted series," Computational Statistics, Springer, vol. 33(1), pages 443-465, March.
    6. Masaki Narukawa, 2016. "Semiparametric Whittle estimation of a cyclical long-memory time series based on generalised exponential models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 272-295, June.
    7. Artiach, Miguel, 2012. "Leverage, skewness and amplitude asymmetric cycles," MPRA Paper 41267, University Library of Munich, Germany.

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