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Local Whittle estimation of the memory parameter in presence of deterministic components

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  • Fabrizio Iacone
Abstract
We discuss the estimation of the order of integration of a fractional process that may be contaminated by a time‐varying deterministic trend or by a break in the mean. We show that in some cases the estimate may still be consistent and asymptotically normally distributed even when the order of magnitude of the spectral density of the fractional process does not dominate the one of the periodogram of the contaminating term. If trimming is introduced, stronger deterministic components may be neglected. The performance of the estimate in small samples is studied in a Monte Carlo experiment.

Suggested Citation

  • Fabrizio Iacone, 2010. "Local Whittle estimation of the memory parameter in presence of deterministic components," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 37-49, January.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:1:p:37-49
    DOI: 10.1111/j.1467-9892.2009.00638.x
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    References listed on IDEAS

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    Cited by:

    1. Laura Mayoral, 2006. "Further Evidence on the Statistical Properties of Real GNP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 901-920, December.
    2. Christensen, Bent Jesper & Varneskov, Rasmus Tangsgaard, 2017. "Medium band least squares estimation of fractional cointegration in the presence of low-frequency contamination," Journal of Econometrics, Elsevier, vol. 197(2), pages 218-244.
    3. Marie Busch & Philipp Sibbertsen, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Econometrics, MDPI, vol. 6(1), pages 1-21, March.
    4. Yohei Yamamoto & Pierre Perron, 2013. "Estimating and testing multiple structural changes in linear models using band spectral regressions," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 400-429, October.
    5. Adam McCloskey, 2013. "Estimation of the long-memory stochastic volatility model parameters that is robust to level shifts and deterministic trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 285-301, May.
    6. Becker, Janis & Leschinski, Christian & Sibbertsen, Philipp, 2019. "Robust Multivariate Local Whittle Estimation and Spurious Fractional Cointegration," Hannover Economic Papers (HEP) dp-660, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    7. Ergemen, Yunus Emre & Rodríguez-Caballero, C. Vladimir, 2023. "Estimation of a dynamic multi-level factor model with possible long-range dependence," International Journal of Forecasting, Elsevier, vol. 39(1), pages 405-430.
    8. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1196-1237, December.
    9. Arteche, Josu & García-Enríquez, Javier, 2017. "Singular Spectrum Analysis for signal extraction in Stochastic Volatility models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 85-98.
    10. Ata Assaf & Luis Alberiko Gil-Alana & Khaled Mokni, 2022. "True or spurious long memory in the cryptocurrency markets: evidence from a multivariate test and other Whittle estimation methods," Empirical Economics, Springer, vol. 63(3), pages 1543-1570, September.
    11. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    12. Javier Hualde & Morten Ørregaard Nielsen, 2022. "Truncated sum-of-squares estimation of fractional time series models with generalized power law trend," CREATES Research Papers 2022-07, Department of Economics and Business Economics, Aarhus University.
    13. Hou, Jie & Perron, Pierre, 2014. "Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations," Journal of Econometrics, Elsevier, vol. 182(2), pages 309-328.
    14. Dalla, Violetta & Giraitis, Liudas & Robinson, Peter M., 2020. "Asymptotic theory for time series with changing mean and variance," Journal of Econometrics, Elsevier, vol. 219(2), pages 281-313.
    15. Becker, Janis & Hollstein, Fabian & Prokopczuk, Marcel & Sibbertsen, Philipp, 2019. "The Memory of Beta Factors," Hannover Economic Papers (HEP) dp-661, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    16. Aeneas Rooch & Ieva Zelo & Roland Fried, 2019. "Estimation methods for the LRD parameter under a change in the mean," Statistical Papers, Springer, vol. 60(1), pages 313-347, February.
    17. Matei Demetrescu & Mehdi Hosseinkouchack, 2022. "Autoregressive spectral estimates under ignored changes in the mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 329-340, March.
    18. Baek, Changryong & Fortuna, Natércia & Pipiras, Vladas, 2014. "Can Markov switching model generate long memory?," Economics Letters, Elsevier, vol. 124(1), pages 117-121.
    19. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2017. "The Memory of Volatility," Hannover Economic Papers (HEP) dp-601, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    20. Leschinski, Christian & Sibbertsen, Philipp, 2017. "Origins of Spurious Long Memory," Hannover Economic Papers (HEP) dp-595, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    21. Leschinski, Christian & Sibbertsen, Philipp, 2018. "The Periodogram of Spurious Long-Memory Processes," Hannover Economic Papers (HEP) dp-632, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    22. Goddard, John & Onali, Enrico, 2012. "Self-affinity in financial asset returns," International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
    23. Iacone Fabrizio & Leybourne Stephen J. & Robert Taylor A.M., 2017. "Testing for a Change in Mean under Fractional Integration," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-8, January.

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