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

Abstract

Please cite this article as: Comte, F., Lacour, C., Rozenholc, Y., Adaptive estimation of the dynamics of a discrete time stochastic volatility model. Journal of Econometrics (2009Econometrics ( ), doi:10.1016Econometrics ( /j.jeconom.2009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. 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: A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTwhere (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 σ 2 when only observations Z1, . . . , Zn are available. We propose to estimate bf and (b 2 + σ 2 )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 σ 2 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.J.E.L. Classification number: C13-C14-C22.

Parametric estimation of hidden stochastic model by contrast minimization and deconvolution

“…This rate of convergence can be improved by assuming some additional regularity conditions on l θ . There is a good discussion about this subject in [CLR10] and [DST11].…”

“…We refer the reader to [VdV98] for a general account on this notion. Furthermore, in this part, we use the contrast function proposed by [CLR10], that is:…”