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

F. Comte, C. Lacour and Y. Rozenholc

Journal of Econometrics, 2010, vol. 154, issue 1, 59-73

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.

Keywords: Adaptive; estimation; Autoregression; Deconvolution; Heteroscedastic; Hidden; Markov; model; Nonparametric; projection; estimator (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:154:y:2010:i:1:p:59-73

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