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Estimation of the Long-Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends

I provide conditions under which the trimmed FDQML estimator, advanced by McCloskey (2010) in the context of fully parametric short-memory models, can be used to estimate the long-memory stochastic volatility model parameters in the presence of additive low-frequency contamination in log-squared returns. The types of lowfrequency contamination covered include level shifts as well as deterministic trends. I establish consistency and asymptotic normality in the presence or absence of such lowfrequency contamination under certain conditions on the growth rate of the trimming parameter. I also provide theoretical guidance on the choice of trimming parameter by heuristically obtaining its asymptotic MSE-optimal rate under certain types of lowfrequency contamination. A simulation study examines the finite sample properties of the robust estimator, showing substantial gains from its use in the presence of level shifts. The finite sample analysis also explores how different levels of trimming affect the parameter estimates in the presence and absence of low-frequency contamination and long-memory.

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Paper provided by Brown University, Department of Economics in its series Working Papers with number 2012-17.

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Date of creation: 2012
Date of revision:
Handle: RePEc:bro:econwp:2012-17
Contact details of provider: Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. 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.
  2. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA.
  3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  4. 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.
  5. Rohit Deo & Clifford Hurvich & Yi Lu, 2005. "Forecasting Realized Volatility Using a Long Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment," Econometrics 0501002, EconWPA.
  6. George Kapetanios & Fotis Papailias, 2011. "Block Bootstrap and Long Memory," Working Papers 679, Queen Mary University of London, School of Economics and Finance.
  7. Zhongjun Qu, 2010. "A Test Against Spurious Long Memory," Boston University - Department of Economics - Working Papers Series WP2010-051, Boston University - Department of Economics.
  8. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
  9. 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.
  10. Perez, Ana & Ruiz, Esther, 2001. "Finite sample properties of a QML estimator of stochastic volatility models with long memory," Economics Letters, Elsevier, vol. 70(2), pages 157-164, February.
  11. 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.
  12. 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.
  13. Per Frederiksen & Morten Orregaard Nielsen, 2008. "Bias-Reduced Estimation of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 496-512, Fall.
  14. D. S. Poskitt, 2008. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 224-250, 03.
  15. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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