[Back]

T. Miazhynskaia:
"Non-Linearity in Volatility Modeling from Classical and Bayesian Perspectives";
Supervisor, Reviewer: E. Dockner, S. Frühwirt-Schnatter; Universität Wien, 2004.

In this thesis, we try to answer the question of how important non-linearity is in volatility modeling. As a tool to describe non-linearity we use neural network based modeling specifying volatility dynamics by a multi-layer perceptron. Neural network models are compared to classical GARCH models.
To stay more general and objective, we consider the linearity issues together with a distributional aspect. We compare the linear models to the non-linear ones under three different conditional density specifications: Gaussian, Student-t and mixture of Gaussians. We estimate our models under two statistical frameworks (maximum likelihood and Bayesian) and analyze their performance with respect to three evaluation criteria: the explanatory power of the models, their forecasting accuracy as well as their performance in a risk management application.
For the empirical analysis we use return series of the Dow Jones Industrial Average index, FTSE 100 and NIKKEI 225 indices, related to three large but distinct financial markets.
The general conclusion is that the conditional density specification plays the determinant role in model performance. The Gaussian distribution clearly underestimates the heavy-tails present in the data. Within the non-Gaussian models, most performance measures favour the mixture models, presented by the recurrent mixture density networks. Non-linearity issues are of much less significance.
Altogether, if a statistical model accounts for non-normality and explains most of the fat tails in the conditional distribution, then there is less need for complex non-linear specifications.