A prime step in the time series forecasting with hybrid methods: The fitness function choice

Artificial Neural Networks (ANN) have been widely used in order to solve the time series forecasting problem. One of its most promising approaches is the combination with other intelligence techniques, as genetic algorithms, evolutionary strategies, etc. The efficiency of these technics, if used correctly, can be very high. Unfortunately, in terms of fitness function, there is still some lacks of experimental (and theoretical) results to help the practitioners to use these technics in order to find better predictions. This paper proposes others fitness functions (instead of conventional MSE based) and presents an experimental investigation of eight different fitness functions for time series prediction based on five well known measures of statistical performance in the literature. Using a hybrid method for tuning of the ANN structure and parameters (a modified genetic Algorithm), an analysis of the final results effects are made according with four relevant time series. This work shows that small changes of the fitness function evaluation can lead to a significantly improved performance.

[1]  G. Lewicki,et al.  Approximation by Superpositions of a Sigmoidal Function , 2003 .

[2]  Tiago A. E. Ferreira,et al.  A hybrid method for tuning neural network for financial time series forecasting , 2008 .

[3]  Fred L. Collopy,et al.  Error Measures for Generalizing About Forecasting Methods: Empirical Comparisons , 1992 .

[4]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[5]  David Zimbra,et al.  A dynamic artificial neural network model for forecasting time series events , 2005 .

[6]  Petros Koumoutsakos,et al.  Accelerating evolutionary algorithms with Gaussian process fitness function models , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[7]  P. McNelis.  Neural networks in finance , 2004 .

[8]  Tiago Alessandro Espínola Ferreira,et al.  A New Intelligent System Methodology for Time Series Forecasting with Artificial Neural Networks , 2008, Neural Processing Letters.

[9]  Francesco Carlo Morabito,et al.  Solar Activity Forecasting by Incorporating Prior Knowledge from Nonlinear Dynamics into Neural Networks , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[10]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[11]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[12]  Wim Hordijk,et al.  A Measure of Landscapes , 1996, Evolutionary Computation.

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

[14]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[15]  Hak-Keung Lam,et al.  Tuning of the structure and parameters of a neural network using an improved genetic algorithm , 2003, IEEE Trans. Neural Networks.

[16]  Ray Jain,et al.  The art of computer systems performance analysis - techniques for experimental design, measurement, simulation, and modeling , 1991, Wiley professional computing.

[17]  Michael Y. Hu,et al.  Forecasting with artificial neural networks: The state of the art , 1997 .

[18]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[19]  Leonard J. Tashman,et al.  Out-of-sample tests of forecasting accuracy: an analysis and review , 2000 .

[20]  P. McNelis.  Neural networks in finance : gaining predictive edge in the market , 2005 .

[21]  Tiago Alessandro Espínola Ferreira,et al.  A New Evolutionary Approach for Time Series Forecasting , 2007, 2007 IEEE Symposium on Computational Intelligence and Data Mining.

[22]  Michael P. Clements,et al.  On the limitations of comparing mean square forecast errors , 1993 .

[23]  D. J. Bartholomew,et al.  Time Series Analysis Forecasting and Control , 1971 .

[24]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[25]  Mohammad Bagher Menhaj,et al.  Training feedforward networks with the Marquardt algorithm , 1994, IEEE Trans. Neural Networks.

[26]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[27]  Kenneth A. De Jong,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods on the Choice of the Offspring Population Size in Evolutionary Algorithms on the Choice of the Offspring Population Size in Evolutionary Algorithms , 2004 .