Adaptive estimation of the dynamics of a discrete time stochastic volatility model |
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Authors: | F Comte C Lacour Y Rozenholc |
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Institution: | 1. Université Paris Descartes, MAP5, UMR CNRS 8145, France;2. Laboratoire de Probabilités et Statistique, Université Paris Sud-Orsay, France |
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Abstract: | This paper is concerned with the discrete time stochastic volatility model Yi=exp(Xi/2)ηi, Xi+1=b(Xi)+σ(Xi)ξi+1, where only (Yi) is observed. The model is rewritten as a particular hidden model: Zi=Xi+εi, Xi+1=b(Xi)+σ(Xi)ξi+1, where (ξi) and (εi) are independent sequences of i.i.d. noise. Moreover, the sequences (Xi) and (εi) are independent and the distribution of ε is known. Then, our aim is to estimate the functions b and σ2 when only observations Z1,…,Zn are available. We propose to estimate bf and (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 b and σ2 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. |
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Keywords: | C13 C14 C22 |
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