Technical Reports - Query Results

ÖFAI-TR-98-28 ( 198kB g-zipped PostScript file,  627kB PDF file)

A Symbolic Dynamics Approach to Volatility Prediction

Peter Tino, Christian Schittenkopf, Georg Dorffner, Engelbert Dockner

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.

Keywords: Variable Memory Length Markov Models, Iterative Function Systems, Volatility prediction

Citation: Tino P., Schittenkopf C., Dorffner G., Dockner E.J.: A Symbolic Dynamics Approach to Volatility Prediction, in Y.S. Abu-Mostafa, B. LeBaron, A.W. Lo, A.S. Weigend. (eds): Computational Finance 99, MIT Press, Cambridge, MA, 2000, pp. 137-151.