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.