Non-linear financial time series forecasting application to the Bel 20 stock market index

We developed in this paper a method to predict time series with non-linear tools. The specificity of the method is to use as much information as possible as input to the model (many past values of the series, many exogenous variables), to compress this information (by a non-linear method) in order to obtain a state vector of limited size, facilitating the subsequent regression and the generalization ability of the forecasting algorithm and to fit a non-linear regressor (here a RBF neural network) on the reduced vectors. We show that this method is able to find non-linear relationships in artificial and real-world financial series. On a difficult task, which consists in forecasting the tendency of the Bel 20 stock market index, we show that this method improves the results compared both to linear models and to non-linear ones where the non-linear compression is not used.

[1]  Floris Takens,et al.  On the numerical determination of the dimension of an attractor , 1985 .

[2]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[3]  Michel Verleysen,et al.  An optimized RBF network for approximation of functions , 1994, ESANN.

[4]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[5]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[6]  Lennart Ljung,et al.  Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..

[7]  A. N. Burgess.  Non-linear model identification and statistical significance tests and their application to financial modelling , 1995 .

[8]  David S. Broomhead,et al.  Multivariable Functional Interpolation and Adaptive Networks , 1988, Complex Syst..

[9]  A. Lo,et al.  Data-Snooping Biases in Tests of Financial Asset Pricing Models , 1989 .

[10]  Jeanny Hérault,et al.  Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets , 1997, IEEE Trans. Neural Networks.

[11]  Theiler.  Statistical precision of dimension estimators. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[12]  Teuvo Kohonen,et al.  In: Self-organising Maps , 1995 .

[13]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[14]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[15]  Geoffrey E. Hinton,et al.  Learning representations by back-propagation errors, nature , 1986 .

[16]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[17]  A. Neil Burgess,et al.  Neural networks in financial engineering: a study in methodology , 1997, IEEE Trans. Neural Networks.

[18]  L. Bachelier.  Le jeu, la chance et le hasard , 1914 .

[19]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[20]  B. LeBaron,et al.  Simple Technical Trading Rules and the Stochastic Properties of Stock Returns , 1992 .

[21]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[22]  F. Eugene.  FAMA, . The Behavior of Stock-Market Prices, Journal of Business, , . , 1965 .

[23]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[24]  H. White,et al.  Data‐Snooping, Technical Trading Rule Performance, and the Bootstrap , 1999 .

[25]  Lennart Ljung,et al.  Nonlinear Black Box Modeling in System Identification , 1995 .

[26]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[27]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[28]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .