We consider the problem of predicting the direction of daily volatility changes in the Dow Jones Industrial Average (DJIA). This is accomplished by quantizing a series of historic volatility changes into a symbolic stream over 2 or 4 symbols. We compare predictive performance of the classical fixed-order Markov models with that of a novel approach to variable memory length prediction (called prediction fractal machine, or PFM) which is able to select very specific deep prediction contexts (whenever there is a sufficient support for such contexts in the training data). We learn that daily volatility changes of the DJIA only exhibit rather shallow finite memory structure. On the other hand, a careful selection of quantization cut values can strongly enhance predictive power of symbolic schemes. Results on 12 non-overlapping epochs of the DJIA strongly suggest that PFMs can outperform both traditional Markov models and (continuous-valued) GARCH models in the task of predicting volatility one time-step ahead. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Diss. Univ. Hamburg, 1998.

Master-Arbeit Univ. St. Gallen, 2008.

We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuous-state branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Dresden, Techn. Univ., Diss., 2000.

Zugl.: Augsburg, Univ., Habil.-Schr., 2002.

Habil.-Schr. Univ. Augsburg, 2002.

Universiẗat, Diss--Köln, 2007.

Zugl.: Tübingen, Univ., Diss.

Frankfurt (Main), University, Diss., 2008.