This paper is concerned with the discrete time stochastic volatility model , , where only is observed. The model is re-written as a particular hidden model: , , where and are independent sequences of i.i.d. noise. Moreover, the sequences and are independent and the distribution of is known. Then, our aim is to estimate the functions and when only observations are available. We propose to estimate and and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces. By ratio strategy, estimators of and 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.