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Semi-Parametric Comparison of Stochastic Volatility Models using Realized Measures

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  • Valentina Corradi
  • Walter Distaso

Abstract

This paper proposes a procedure to test for the correct specification of the functional form of the volatility process within the class of eigenfunction stochastic volatility models. The procedure is based on the comparison of the moments of realized volatility measures with the corresponding ones of integrated volatility implied by the model under the null hypothesis.We first provide primitive conditions on the measurement error associated with the realized measure, which allow to construct asymptotically valid specification tests.Then we establish regularity conditions under which the considered realized measures, namely, realized volatility, bipower variation, and modified subsampled realized volatility, satisfy the given primitive assumptions.Finally, we provide an empirical illustration based on three stocks from the Dow Jones Industrial Average. Copyright 2006, Wiley-Blackwell.

Suggested Citation

  • Valentina Corradi & Walter Distaso, 2006. "Semi-Parametric Comparison of Stochastic Volatility Models using Realized Measures," Review of Economic Studies, Oxford University Press, vol. 73(3), pages 635-667.
  • Handle: RePEc:oup:restud:v:73:y:2006:i:3:p:635-667
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    File URL: http://hdl.handle.net/10.1111/j.1467-937X.2006.00390.x
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    Cited by:

    1. Corradi, Valentina & Distaso, Walter & Fernandes, Marcelo, 2013. "Conditional alphas and realized betas," Textos para discussão 341, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    2. Asai, Manabu & McAleer, Michael & Medeiros, Marcelo C., 2012. "Modelling and forecasting noisy realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 217-230, January.
    3. Ishida, I. & McAleer, M.J. & Oya, K., 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 VIX," Econometric Institute Research Papers EI 2011-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Indirect inference with time series observed with error," CREATES Research Papers 2014-57, Department of Economics and Business Economics, Aarhus University.
    5. Anne Brix & Asger Lunde, 2015. "Prediction-based estimating functions for stochastic volatility models with noisy data: comparison with a GMM alternative," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(4), pages 433-465, October.
    6. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models : from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    7. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    8. Isao Ishida & Michael McAleer & Kosuke Oya, 2011. "Estimating the leverage parameter of continuous-time stochastic volatility models using high frequency S&P 500 and VIX," Managerial Finance, Emerald Group Publishing, vol. 37(11), pages 1048-1067, September.
    9. Bregantini, Daniele, 2013. "Moment-based estimation of stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4755-4764.
    10. Papanicolaou, Alex & Giesecke, Kay, 2016. "Variation-based tests for volatility misspecification," Journal of Econometrics, Elsevier, vol. 191(1), pages 217-230.
    11. Li, Jia & Todorov, Viktor & Tauchen, George, 2016. "Inference theory for volatility functional dependencies," Journal of Econometrics, Elsevier, vol. 193(1), pages 17-34.
    12. Corradi, Valentina & Distaso, Walter & Mele, Antonio, 2013. "Macroeconomic determinants of stock volatility and volatility premiums," Journal of Monetary Economics, Elsevier, vol. 60(2), pages 203-220.
    13. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 15(3), pages 94-138.
    14. Linton, Oliver & Whang, Yoon-Jae & Yen, Yu-Min, 2016. "A nonparametric test of a strong leverage hypothesis," Journal of Econometrics, Elsevier, vol. 194(1), pages 153-186.
    15. repec:eee:econom:v:203:y:2018:i:2:p:223-240 is not listed on IDEAS
    16. Jia Li & Andrew J. Patton, 2013. "Asymptotic Inference about Predictive Accuracy Using High Frequency Data," Working Papers 13-27, Duke University, Department of Economics.
    17. Zu, Yang, 2015. "Nonparametric specification tests for stochastic volatility models based on volatility density," Journal of Econometrics, Elsevier, vol. 187(1), pages 323-344.
    18. Asger Lunde & Anne Floor Brix, 2013. "Estimating Stochastic Volatility Models using Prediction-based Estimating Functions," CREATES Research Papers 2013-23, Department of Economics and Business Economics, Aarhus University.

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