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This paper is concerned with the discrete time stochastic volatility model Yi=exp(Xi/2)ηiYi=exp(Xi/2)ηi, Xi+1=b(Xi)+σ(Xi)ξi+1Xi+1=b(Xi)+σ(Xi)ξi+1, where only (Yi)(Yi) is observed. The model is rewritten as a particular hidden model: Zi=Xi+εiZi=Xi+εi, Xi+1=b(Xi)+σ(Xi)ξi+1Xi+1=b(Xi)+σ(Xi)ξi+1, where (ξi)(ξi) and (εi)(εi) are independent sequences of i.i.d. noise. Moreover, the sequences (Xi)(Xi) and (εi)(εi) are independent and the distribution of εε is known. Then, our aim is to estimate the functions bb and σ2σ2 when only observations Z1,…,ZnZ1,,Zn are available. We propose to estimate bfbf and (b22)f(b2+σ2)f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces. By ratio strategy, estimators of bb and σ2σ2 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.  相似文献   

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