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Adaptive estimation of the dynamics of a discrete time stochastic volatility model

Author

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  • Comte, F.
  • Lacour, C.
  • Rozenholc, Y.

Abstract

This paper is concerned with the discrete time stochastic volatility model Yi=exp(Xi/2)[eta]i, Xi+1=b(Xi)+[sigma](Xi)[xi]i+1, where only (Yi) is observed. The model is rewritten as a particular hidden model: Zi=Xi+[epsilon]i, Xi+1=b(Xi)+[sigma](Xi)[xi]i+1, where ([xi]i) and ([epsilon]i) are independent sequences of i.i.d. noise. Moreover, the sequences (Xi) and ([epsilon]i) are independent and the distribution of [epsilon] is known. Then, our aim is to estimate the functions b and [sigma]2 when only observations Z1,...,Zn are available. We propose to estimate bf and (b2+[sigma]2)f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces. By ratio strategy, estimators of b and [sigma]2 are then deduced. The mean square risk of the resulting estimators are studied and their rates are discussed. Lastly, simulation experiments are provided: constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples.

Suggested Citation

  • Comte, F. & Lacour, C. & Rozenholc, Y., 2010. "Adaptive estimation of the dynamics of a discrete time stochastic volatility model," Journal of Econometrics, Elsevier, vol. 154(1), pages 59-73, January.
    • Handle: RePEc:eee:econom:v:154:y:2010:i:1:p:59-73
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    2. Hong, Han & Tamer, Elie, 2003. "A simple estimator for nonlinear error in variable models," Journal of Econometrics, Elsevier, vol. 117(1), pages 1-19, November.
    3. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    4. Lacour, Claire, 2008. "Nonparametric estimation of the stationary density and the transition density of a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 232-260, February.
    5. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
    6. Ioannides, D. A. & Alevizos, P. D., 1997. "Nonparametric regression with errors in variables and applications," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 35-43, February.
    7. Comte, F. & Rozenholc, Y., 2002. "Adaptive estimation of mean and volatility functions in (auto-)regressive models," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 111-145, January.
    8. Fan, Jianqing & Masry, Elias, 1992. "Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 237-271, November.
    9. Koo, Ja-Yong & Lee, Kee-Won, 1998. "B-spline estimation of regression functions with errors in variable," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 57-66, September.
    10. Arnaud Gloter, 2007. "Efficient estimation of drift parameters in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(4), pages 495-519, October.
    11. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    12. Reno, Roberto, 2006. "Nonparametric estimation of stochastic volatility models," Economics Letters, Elsevier, vol. 90(3), pages 390-395, March.
    13. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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    Cited by:

    1. Salima El Kolei, 2013. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1031-1081, November.
    2. El Kolei, Salima & Pelgrin, Florian, 2017. "Parametric inference of autoregressive heteroscedastic models with errors in variables," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 63-70.

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