Abstract
A crucial problem in non-linear time series forecasting is to determine its auto-regressive order, in particular when the prediction method is non-linear. We show in this paper that this problem is related to the fractal dimension of the time series, and suggest using the Curvilinear Component Analysis (CCA) to project the data in a non-linear way on a space of adequately chosen dimension, before the prediction itself. The performances of this method are illustrated on the SBF 250 index.
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Alligood K. T, Sauer T. D., Yorke J. A.: Chaos: An Introduction to Dynamical Systems. Springer-Verlag, New York (1997), pp. 537–556
Box G.E.P., Jenkins G.: Time Series analysis: Forecasting and Control. Cambridge University Press (1976)
Demartines P., Hérault J.: Curvilinear Component Analysis: A self-organizing neural network for nonlinear mapping of data sets. IEEE Trans. on Neural Networks 8(1) (1997) 148–154
Grassberger P., Procaccia I.: Measuring the Strangeness of Strange Attractors. Physica D56 (1983) 189–208
Ljung L.: System Identification-Theory for User. Prentice-Hall (1987)
Tackens F.: On the numerical Determination of the dimension of an attractor. In: Lecture Notes in Mathematics Vol. 1125, Springer-Verlag (1985) 99–106
Theiler J.: Statistical Precision of Dimension Estimators. Phys. Rev. A41 (1990) 3038–3051
Weigend A. S., Gershenfeld N.A.: Times Series Prediction: Forcasting the future and Understanding the Past. Addison-Wesley Publishing Company (1994)
Xiangdong He, Haruhiko Asada: A New Method for Identifying Orders of Input-Output Models for Nonlinear Dynamic Systems. In: Proc. of the American Control Conf., San Francisco (CA) (1993) 2520–2523
Burgess A.N.: Non-linear Model Identification and Statistical Significance Tests and their Application to Financial Modelling. In: Artificial Neural Networks, Inst. Elect. Eng. Conf., June (1995)
Fama E.: Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance XXV No 2 (1970) 383–417
Refenes A. N., Burgess A. N. and Bentz Y.: Neural Networks in Financial Engineering: A Study in Methodology. IEEE Transactions on Neural Networks 8 (6) (1997) 1222–1267
Verleysen M., Hlavačkova K.: An Optimized RBF Network for Approximation of Functions. In: Proc of European Symposium on Artificial Neural Networks, Brussels (Belgium), April 1994, D facto publications (Brussels).
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Verleysen, M., de Bodt, E., Lendasse, A. (1999). Forecasting financial time series through intrinsic dimension estimation and non-linear data projection. In: Mira, J., Sánchez-Andrés, J.V. (eds) Engineering Applications of Bio-Inspired Artificial Neural Networks. IWANN 1999. Lecture Notes in Computer Science, vol 1607. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0100527
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DOI: https://doi.org/10.1007/BFb0100527
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