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Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns

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  • Pierre Perron

    ()
    (Department of Economics, Boston University)

  • Rasmus T. Varneskov

    ()
    (Department of Economics and Business, Aarhus University)

Abstract

We consider modeling and forecasting a variety of asset return volatility series by adding a random level shift component to the usual long-memory ARFIMA model. We propose a parametric state space model with an accompanying estimation and forecasting framework that combines long memory and level shifts by decomposing the underlying process into a simple mixture model and ARFIMA dynamics. The Kalman filter is used to construct the likelihood function after augmenting the probability of states by a mixture of normally distributed processes. The forecasts are constructed by exploiting the information in the Kalman recursions. The adequacy of the estimation methodology is shown through a simulation study. We apply our model to volatility series categorized in two groups: high frequency based series (tick-by-tick SPY trades and realized volatility on the S&P 500 and 30-year Treasury Bond futures) and longer spans of log-absolute daily returns (S&P 500 returns, Dollar-Aus and Dollar-Yen exchange rates). The full sample estimates show that level shifts are present in all series. A genuine long-memory component is present in measures of volatility constructed using high-frequency data. On the other hand, volatility series proxied by log daily absolute returns are characterized by a remaining short-memory component that is nearly uncorrelated once the level shifts are accounted for. We conduct extensive out-of-sample forecast evaluations and compare the results with four popular competing models. Interestingly, our ARFIMA model with random level shifts is the only model that consistently belongs to the 10% Model Con dence Set of Hansen et al. (2011) for both pairwise and joint comparisons. It does so for all series, forecasting periods, forecast horizons, forecast evaluation criteria and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.

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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 WP2011-050.

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Length: 42 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:bos:wpaper:wp2011-050

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References

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  1. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
  2. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(06), pages 1196-1237, December.
  3. Roxana Chiriac & Valeri Voev, 2008. "Modelling and Forecasting Multivariate Realized Volatility," CREATES Research Papers 2008-39, School of Economics and Management, University of Aarhus.
  4. Sun, Yixiao & Phillips, Peter C. B., 2003. "Nonlinear log-periodogram regression for perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 115(2), pages 355-389, August.
  5. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
  6. Iliyan GEORGIEV, 2002. "Functional Weak Limit Theory for Rare Outlying Events," Economics Working Papers ECO2002/22, European University Institute.
  7. Rasmus Tangsgaard Varneskov & Valeri Voev, 2010. "The Role of Realized Ex-post Covariance Measures and Dynamic Model Choice on the Quality of Covariance Forecasts," CREATES Research Papers 2010-45, School of Economics and Management, University of Aarhus.
  8. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, 07.
  9. 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.
  10. Martin, V.L. & Wilkins, N.P., 1997. "Indirect Estimation of Arfima and Varfima Models," Department of Economics - Working Papers Series 547, The University of Melbourne.
  11. Wen-Jen Tsay & Wolfgang Härdle, 2007. "A Generalized ARFIMA Process with Markov-Switching Fractional Differencing Parameter," SFB 649 Discussion Papers SFB649DP2007-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  12. Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
  14. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
  15. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
  16. 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.
  17. Nunes, Luis C. & Newbold, Paul & Chung-Ming Kuan, 1996. "Spurious number of breaks," Economics Letters, Elsevier, vol. 50(2), pages 175-178, February.
  18. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  19. Vasco J. Gabriel & Luis F. Martins, 2004. "On the forecasting ability of ARFIMA models when infrequent breaks occur," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 455-475, December.
  20. Tatsuma Wada & Pierre Perron, 2006. "State Space Model with Mixtures of Normals: Specifications and Applications to International Data," Boston University - Department of Economics - Working Papers Series WP2006-029, Boston University - Department of Economics.
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