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Adaptive estimation of the dynamics of a discrete time stochastic volatility model
[journal article]
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,... view more
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.... view less
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
DOI
https://doi.org/10.1016/j.jeconom.2009.07.001
Status
Postprint; peer reviewed
Licence
PEER Licence Agreement (applicable only to documents from PEER project)