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Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends

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Abstract

We propose estimators of the memory parameter of a time series that are robust to a wide variety of random level shift processes, deterministic level shifts and deterministic time trends. The estimators are simple trimmed versions of the popular log-periodogram regression estimator that employ certain sample size-dependent and, in some cases, data-dependent trimmings which discard low-frequency components. We also show that a previously developed trimmed local Whittle estimator is robust to the same forms of data contamination. Regardless of whether the underlying long/shortmemory process is contaminated by level shifts or deterministic trends, the estimators are consistent and asymptotically normal with the same limiting variance as their standard untrimmed counterparts. Simulations show that the trimmed estimators perform their intended purpose quite well, substantially decreasing both finite sample bias and root mean-squared error in the presence of these contaminating components. Furthermore, we assess the tradeoffs involved with their use when such components are not present but the underlying process exhibits strong short-memory dynamics or is contaminated by noise. To balance the potential finite sample biases involved in estimating the memory parameter, we recommend a particular adaptive version of the trimmed log-periodogram estimator that performs well in a wide variety of circumstances. We apply the estimators to stock market volatility data to find that various time series typically thought to be long-memory processes actually appear to be short or very weak long-memory processes contaminated by level shifts or deterministic trends.

Suggested Citation

  • Adam McCloskey & Pierre Perron, 2012. "Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends," Working Papers 2012-15, Brown University, Department of Economics.
  • Handle: RePEc:bro:econwp:2012-15
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Tzouras, Spilios & Anagnostopoulos, Christoforos & McCoy, Emma, 2015. "Financial time series modeling using the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 50-68.
    6. repec:gam:jecnmx:v:6:y:2018:i:1:p:13-:d:135826 is not listed on IDEAS
    7. Kruse, Robinson, 2015. "A modified test against spurious long memory," Economics Letters, Elsevier, vol. 135(C), pages 34-38.
    8. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    9. Pierre Perron & Wendong Shi, 2014. "Temporal Aggregation, Bandwidth Selection and Long Memory for Volatility Models," Boston University - Department of Economics - Working Papers Series wp2014-009, Boston University - Department of Economics.
    10. repec:eee:ecofin:v:42:y:2017:i:c:p:393-420 is not listed on IDEAS
    11. 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.
    12. Marie Busch & Philipp Sibbertsen, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Econometrics, MDPI, Open Access Journal, vol. 6(1), pages 1-21, March.
    13. Rasmus Tangsgaard Varneskov & Pierre Perron, 2011. "Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns," CREATES Research Papers 2011-26, Department of Economics and Business Economics, Aarhus University.
    14. Gabriel Rodríguez, 2016. " Modeling Latin-American Stock and Forex Markets Volatility: Empirical Application of a Model with Random Level Shifts and Genuine Long Memory [Modelando la volatilidad de los mercados bursátiles y ca," Documentos de Trabajo / Working Papers 2016-416, Departamento de Economía - Pontificia Universidad Católica del Perú.
    15. Claudio Morana, 2013. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks: New Insights on the US OIS SPreads Term Structure," Working Papers 233, University of Milano-Bicocca, Department of Economics, revised Feb 2013.
    16. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 0404. "Does the ARFIMA really shift?," CREATES Research Papers 2017-16, Department of Economics and Business Economics, Aarhus University.
    17. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    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.

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    Keywords

    long-memory processes; semiparametric estimators; level shifts; structural change; deterministic trends;

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