In this thesis, we investigate a variety of stochastic models for volatilityprediction in financial time series. We compare two non-parametricvolatility models with the standard GARCH(1,1) model. In the firstnonparametric GARCH modeling, we consider the functional gradient descent(FGD) method in Audrino and Buhlmann (2009) to find out the optimalB-spline structure in order to get the maximum likelihood. In the secondnonparametric GARCH modeling, we consider the additive autoregressivestructure (aGARCH) with components linked together by a dynamiccoefficient proposed in Wang, et al. (2011). B-spline smoothing method is adopted in both algorithms. The performance of both the parametric and non-parametric GARCH models is investigated by means of simulation studies and an application to S&P 500 index return study and Apple stock return study.They both demonstrate strong improvement in volatility prediction.