Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5096911 | Journal of Econometrics | 2010 | 15 Pages |
Abstract
This paper is concerned with the discrete time stochastic volatility model Yi=exp(Xi/2)ηi, Xi+1=b(Xi)+Ï(Xi)ξi+1, where only (Yi) is observed. The model is rewritten as a particular hidden model: Zi=Xi+εi, Xi+1=b(Xi)+Ï(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 Ï2 when only observations Z1,â¦,Zn are available. We propose to estimate bf and (b2+Ï2)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 Ï2 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
F. Comte, C. Lacour, Y. Rozenholc,