Nonparametric GARCH models for financial volatility

Abstract

In this thesis, we investigate a variety of stochastic models for volatility prediction in financial time series. We compare two non-parametric volatility models with the standard GARCH(1,1) model. In the first nonparametric GARCH modeling, we consider the functional gradient descent (FGD) method in Audrino and Buhlmann (2009) to find out the optimal B-spline structure in order to get the maximum likelihood. In the second nonparametric GARCH modeling, we consider the additive autoregressive structure (aGARCH) with components linked together by a dynamic coefficient 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.