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@article{ Comte2009, title = {Adaptive estimation of the dynamics of a discrete time stochastic volatility model}, author = {Comte, F. and Lacour, C. and Rozenholc, Y.}, journal = {Journal of Econometrics}, number = {1}, pages = {59-73}, volume = {154}, year = {2009}, doi = {https://doi.org/10.1016/j.jeconom.2009.07.001}, urn = {https://nbn-resolving.org/urn:nbn:de:0168-ssoar-261755}, 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.}, }