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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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    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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