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

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Author Info

  • Pierre Perron

    ()
    (Department of Economics, Boston University)

  • Adam McCloskey

    ()
    (Department of Economics, Boston University)

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 de- terministic 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. Regardless of whether the underlying long/short-memory process is contaminated by level shifts or deterministic trends, our estimators are shown to be consistent and asymptotically normal with the same limiting variance as the standard log-periodogram estimator. An extensive simulation study shows that our estimators perform their in- tended purpose quite well, substantially decreasing both nite sample bias and root mean-squared error in the presence of these contaminating components. Furthermore, we assess the tradeo s 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 nite sample biases involved in estimating the mem- ory parameter, we recommend a particular version of our estimators that performs well in a wide variety of circumstances. Finally, we apply our estimators to stock market volatility and hydrological data to nd that many of the time series typically thought to be long-memory processes actually appear to be short-memory processes contaminated by level shifts or deterministic trends.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2010-048.

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Length: 59 pages
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:bos:wpaper:wp2010-048

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Related research

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

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References

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  1. Hurvich, Clifford & Lang, Gabriel & Soulier, Philippe, 2005. "Estimation of Long Memory in the Presence of a Smooth Nonparametric Trend," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 853-871, September.
  2. Per Frederiksen & Frank S. Nielsen & Morten Ørregaard Nielsen, 2008. "Local polynomial Whittle estimation of perturbed fractional processes," CREATES Research Papers 2008-29, School of Economics and Management, University of Aarhus.
  3. Haldrup, Niels & Nielsen, Morten Orregaard, 2007. "Estimation of fractional integration in the presence of data noise," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3100-3114, March.
  4. Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
  5. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
  6. Yixiao Sun & Peter C.B. Phillips, 2002. "Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes," Cowles Foundation Discussion Papers 1366, Cowles Foundation for Research in Economics, Yale University.
  7. Yang K. Lu & Pierre Perron, 2008. "Modeling and Forecasting Stock Return Volatility Using a Random Level Shift Model," Boston University - Department of Economics - Working Papers Series wp2008-012, Boston University - Department of Economics.
  8. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is what?: A simple time-domain test of long-memory vs. structural breaks," Economics Working Papers 954, Department of Economics and Business, Universitat Pompeu Fabra.
  9. Francis X. Diebold & Atsushi Inoue, 2000. "Long Memory and Regime Switching," NBER Technical Working Papers 0264, National Bureau of Economic Research, Inc.
  10. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  11. Iliyan GEORGIEV, 2002. "Functional Weak Limit Theory for Rare Outlying Events," Economics Working Papers ECO2002/22, European University Institute.
  12. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  13. René Garcia & Pierre Perron, 1995. "An Analysis of the Real Interest Rate Under Regime Shifts," CIRANO Working Papers 95s-05, CIRANO.
  14. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
  15. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
  16. Smith, Aaron, 2005. "Level Shifts and the Illusion of Long Memory in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 321-335, July.
  17. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
  18. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  19. 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, 01.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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, 05.
  4. Pierre Perron & Rasmus T. Varneskov, 2011. "Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns," Boston University - Department of Economics - Working Papers Series WP2011-050, Boston University - Department of Economics.

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