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Localized Realized Volatility Modelling

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  • Ying Chen
  • Wolfgang Härdle
  • Uta Pigorsch

Abstract

With the recent availability of high-frequency Financial data the long range dependence of volatility regained researchers' interest and has lead to the consideration of long memory models for realized volatility. The long range diagnosis of volatility, however, is usually stated for long sample periods, while for small sample sizes, such as e.g. one year, the volatility dynamics appears to be better described by short-memory processes. The ensemble of these seemingly contradictory phenomena point towards short memory models of volatility with nonstationarities, such as structural breaks or regime switches, that spuriously generate a long memory pattern (see e.g. Diebold and Inoue, 2001; Mikosch and Starica, 2004b). In this paper we adopt this view on the dependence structure of volatility and propose a localized procedure for modeling realized volatility. That is at each point in time we determine a past interval over which volatility is approximated by a local linear process. Using S&P500 data we find that our local approach outperforms long memory type models in terms of predictability.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2009-003.

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Length: 30 pages
Date of creation: Jan 2009
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2009-003

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Keywords: Localized Autoregressive Modeling; Realized Volatility; Adaptive Procedure;

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References

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  1. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  2. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  3. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  6. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  7. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Estimating quadratic variation using realised variance," Economics Series Working Papers 2001-W20, University of Oxford, Department of Economics.
  8. Francis X. Diebold & Atsushi Inoue, 2000. "Long Memory and Regime Switching," NBER Technical Working Papers 0264, National Bureau of Economic Research, Inc.
  9. Thomas Mikosch & Catalin Starica, 2004. "Changes of structure in financial time series and the GARCH model," Econometrics 0412003, EconWPA.
  10. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
  11. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  12. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
  13. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  14. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  15. Doornik Jurgen A & Ooms Marius, 2004. "Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.
  16. Denis Belomestny & Vladimir Spokoiny, 2006. "Spatial aggregation of local likelihood estimates with applications to classification," SFB 649 Discussion Papers SFB649DP2006-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  17. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
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  19. repec:oxf:wpaper:264 is not listed on IDEAS
  20. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  21. 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.
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Citations

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Cited by:
  1. Lutz, Benjamin Johannes & Pigorsch, Uta & Rotfuß, Waldemar, 2013. "Nonlinearity in cap-and-trade systems: The EUA price and its fundamentals," ZEW Discussion Papers 13-001 [rev.], ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  2. Audrino, Francesco & Knaus, Simon, 2012. "Lassoing the HAR model: A Model Selection Perspective on Realized Volatility Dynamics," Economics Working Paper Series 1224, University of St. Gallen, School of Economics and Political Science.
  3. Golosnoy, Vasyl & Ragulin, Sergiy & Schmid, Wolfgang, 2011. "CUSUM control charts for monitoring optimal portfolio weights," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2991-3009, November.
  4. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Wolfgang Karl Härdle & Nikolaus Hautsch & Andrija Mihoci, 2012. "Local Adaptive Multiplicative Error Models for High-Frequency Forecasts," SFB 649 Discussion Papers SFB649DP2012-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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