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The Analysis of Stochastic Volatility in the Presence of Daily Realized Measures

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  • Siem Jan Koopman
  • Marcel Scharth

Abstract

We develop a systematic framework for the joint modeling of returns and multiple daily realized measures. We assume a linear state space representation for the log realized measures, which are noisy and biased estimates of the log daily integrated variance, at least due to Jensen's inequality. We incorporate filtering methods for the estimation of the latent log-volatility process. The dependence between daily returns and realized measurement errors leads us to develop a two-step estimation method for all parameters in our model specification. The estimation method is computationally straightforward even when the stochastic volatility model has non-Gaussian return innovations and leverage effects. Our extensive empirical study for nine Dow Jones stock return series reveals that measurement errors become significantly smaller after filtering and that the forecasts from our model outperforms those from a set of recently developed alternatives. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

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File URL: http://hdl.handle.net/10.1093/jjfinec/nbs016
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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 11 (2012)
Issue (Month): 1 (December)
Pages: 76-115

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Handle: RePEc:oup:jfinec:v:11:y:2012:i:1:p:76-115

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  1. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten �rregaard Nielsen, 2010. "Continuous-time models, realized volatilities, and testable distributional implications for daily stock returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 233-261.
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  5. David E. Allen & Michael McAleer & Marcel Scharth, 2013. "Realized volatility risk," Documentos del Instituto Complutense de Análisis Económico 2013-26, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
  6. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
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  10. Asai, M. & McAleer, M.J. & Medeiros, M.C., 2008. "Asymmetry and leverage in realized volatility," Econometric Institute Research Papers EI 2008-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  11. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
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  15. Geert Mesters & Siem Jan Koopman & Marius Ooms, 2011. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Tinbergen Institute Discussion Papers 11-090/4, Tinbergen Institute.
  16. Gonçalves, Sílvia & Meddahi, Nour, 2011. "Box-Cox transforms for realized volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 129-144, January.
  17. Siem Jan Koopman & Andre Lucas & Marcel Scharth, 2011. "Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models," Tinbergen Institute Discussion Papers 11-057/4, Tinbergen Institute, revised 27 Jan 2012.
  18. Eric Hillebrand & Marcelo Medeiros, 2010. "The Benefits of Bagging for Forecast Models of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 29(5-6), pages 571-593.
  19. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
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  22. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, 03.
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  26. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
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