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Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends

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  • Mccloskey, Adam
  • Perron, Pierre

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

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 29 (2013)
Issue (Month): 06 (December)
Pages: 1196-1237

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Handle: RePEc:cup:etheor:v:29:y:2013:i:06:p:1196-1237_00

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  1. Garcia, Rene & Perron, Pierre, 1996. "An Analysis of the Real Interest Rate under Regime Shifts," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 111-25, February.
  2. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
  3. 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.
  4. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
  5. Francis X. Diebold & Atsushi Inoue, 2000. "Long Memory and Regime Switching," NBER Technical Working Papers 0264, National Bureau of Economic Research, Inc.
  6. Smith, Aaron D., 2004. "Level Shifts and the Illusion of Long Memory in Economic Time Series," Working Papers 11974, University of California, Davis, Department of Agricultural and Resource Economics.
  7. Iliyan GEORGIEV, 2002. "Functional Weak Limit Theory for Rare Outlying Events," Economics Working Papers ECO2002/22, European University Institute.
  8. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2005. "What is What? A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Working Papers 258, Barcelona Graduate School of Economics.
  9. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
  10. 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.
  11. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  12. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
  13. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  14. 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.
  15. 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.
  16. Per Frederiksen & Frank S. Nielsen & Morten Ørregaard Nielsen, 2009. "Local polynomial Whittle estimation of perturbed fractional processes," Working Papers 1218, Queen's University, Department of Economics.
  17. 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.
  18. 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.
  19. 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.
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Cited by:
  1. 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.
  2. Yohei Yamamoto & Pierre Perron, 2012. "Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions," Global COE Hi-Stat Discussion Paper Series gd12-250, Institute of Economic Research, Hitotsubashi University.
  3. 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, School of Economics and Management, University of Aarhus.
  4. 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.
  5. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, School of Economics and Management, University of Aarhus.

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