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

[journal article]

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

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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 re-written 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.
Classification Economic Statistics, Econometrics, Business Informatics
Free Keywords C13; C14; C22; Adaptive Estimation; Autoregression; Deconvolution; Heteroscedastic; Hidden Markov Model; Nonparametric Projection Estimator
Document language English
Publication Year 2009
Page/Pages p. 59-73
Journal Journal of Econometrics, 154 (2009) 1
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)