Multi Voronoi Nets System for Market Information Processing
by
Marina Resta
D.I.E.M., sez. Matematica Finanziaria,Facolta' di Economia, Universita' di Genova

This paper addresses to the topic of financial forecasting, when responsesfrom more than one artificial neural network are taken into account.

In particular, we refer to Multi Voronoi Information Processing (MVIP) system, where the nets play the role of traders: each net is called to takelong/short positions in the market, according to the perception of future price they have formed during learning procedure over past data; final price comes then out as meeting point among different nets positions. The novelty of this approach relies primarily in the kind of neural architecture employed, and in the way market available information are processed. The key idea is quite simple, and may be briefly summarised as follows. Voronoi nets are a subclass of Topology Representing Networks (TRN), i.e. we deal with competitive learning algorithms [4] [5]. A common goal of these models is to distribute a number of vectors (namely the weights or reference vectors associated to each neuron ) in a high dimensional space in a fashion that should be able to reflect, in one of several ways, the probability distribution of input signals which is implicitly given through sample vectors. These models are good classifiers, and many economical applications are known (see for example [3], and [9]). Recently it has also been pointed on their forecasting capabilities [6], [7], [8]. We move from the results shown in [8], going one step ahead: the efficacy of MVIP system is tested on Down Jones Industrial Average (DJIA) and COMIT30 (*) daily fluctuations, valuing MVIP performances by means of financial criteria. The reason for good performances relies essentially into two features of our method: i ) During learning procedure, reference vectors of each neuron are modified through a truncated parametric gaussian function with coefficient alpha varying in (0,1), hence giving different generalisation capabilities to each net. More correctly, we can think each parameter to correspond to a different tassellation of input space. ii) The choice of parameters in the learning procedure also affects the representation of price fluctuations volatility, which then tends to concentrate more or less on the extremes or on central values. Hence combining Voronoi nets with different learning coefficients can be more performing than using classical econometric stochastic models (GARCH) as well as traditional models for extremes: we give experimental proof by comparing our results with those of GARCH models [1],and those obtained by modelling price fluctuations according to different probability density functions (L-stable, Frechet) generated by applying the Gnedenko-Kolmogorov theorem [2]. This work is organised as follows. In section II we briefly recall Voronoi nets main features. In section III we introduce MVIP and test it on Dow Jones Industrial Average and COMIT30 indexes. In section IV we discuss our results by comparing them, under financial profiles, with results coming from GARCH models as well as by modelling price fluctuations with L-stable and Frechet probability density functions. Finally section V contains conclusive remarks and perspectives for future works. References [1] T. BOLLERSLEV, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 1986, 307-327 [2] B. V. GNEDENKO, A. N. KOLMOGOROV, Limit Distributions for Sums of Independent Random Variables,Addison Wesley, Reading, MA, 1954. [3] S. KASKI, - T. KOHONEN , Exploratory Data Analysis by the Self-Organizing Map: Structures of Welfare and Poverty in the World, Proceedings of the 3rd Conference on Neural Networks in the Capital Markets, London Business School, 1995. [4] T . KOHONEN, Self-Organizing Maps, Springer series in information science, 1997. [5] T. MARTINETZ, K. SCHULTEN, Topology Representing Networks, Neural Networks, Vol. 7, No. 3, 1994 [6] M. RESTA, An hybrid neural network system for trading financial markets, in T.Kohonen-G.J.Deboeck Edrs, Visual Data Explorations in finance with Self Organizing Maps, Finance Series, Springer Verlag London, 1998,106-116. [7] M. RESTA, Hybrid Neural Networks vs Non Linear Time Series Models in Financial Forecasting, accepted at SCFM'99 (Symposium on Soft Computing In Financial Markets), June 22-25, 1999 Rochester Institute of Technology, Rochester, New York (USA). [8] M. RESTA, A topology representing network approach to market price modelling, submitted to WEHIA99 (Workshop on Economics with Heterogeneous Interacting Agents'99, Genoa Italy 4-6 June 1999) [9] C. Serrano-Cinca, Let financial data speak for themselves, in T.Kohonen-G.J.Deboeck Edrs, Visual Data Explorations in finance with Self Organizing Maps, Finance Series, Springer Verlag London, 1998,3-23 (*) COMmercial ITalian bank index: data incorporated in the official stock exchange italian index (MIB30) since October 10th 1994

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Date received: March 1, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacq-18.