Electronic Thesis and Dissertation Repository


Doctor of Philosophy




John Knight


My dissertation consists of three essays focusing on modeling financial asset return and volatility.

The first essay proposes a threshold GARCH model to describe the regime-switching in volatility dynamics of financial asset returns. In the threshold model the switching of regimes is triggered by an observable variable, while volatility follows a GARCH process within each regime. We establish theoretical conditions, which ensure that the return process in the threshold model is strictly stationary, as well as conditions for the existence of finite variance and fourth moment. A simulation study is further conducted to examine the finite sample properties of the maximum likelihood estimator.

The second essay extends our study of the threshold GARCH model to an empirical application. The empirical results support the use of the threshold variable to identify the regime shifts in the volatility process. Especially when VIX is used as the threshold, we are able to separate the clustering of volatile periods corresponding to various financial crises. The threshold GARCH model is able to provide a better volatility forecast in the period of financial crises.

The third essay examines the effect of time structure on the estimation performance of ICA models and provides guidance in applying the ICA model to time series data. We compare the performance of the basic ICA model to the time series ICA model in which the cross-autocovariances are used as a measure to achieve independence. We conduct a simulation study to evaluate the time series ICA model under different time structure assumptions about the underlying components that generate financial time series. Moreover, the empirical results support the use of the time series ICA model.