Summary
This paper explores the idea of using a Genetic algorithm (GA) to solve the problem of subset model selection within the class of bilinear time series processes. The research is based on the concept of evolution theory as well as that of survival of the fittest. We use the AIC, BIG or SBC criteria as the adaptive functions to measure the degree of fitness. During the GA process, the best-fitted population is selected and certain characteristics are translated into the next generation. Simulation results demonstrate that genetic-based learning can effectively work out a pattern of the underlying time series. Finally, we illustrate how the GA can be applied successfully to subset selection in a bilinear time series via several examples and a simulation study.
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References
Akaike, H. (1973) Information theory and an extension of the maximum likelihood principle, Proc. 2nd International Symposium on Information Theory, Edited by Petrov, B. N. and Csaki, F., Akademiai Kiado, Budapest, 267–281.
Akaike, H. (1974) A new look at the statistical model identification, IEEE Transactions on Automatic Control, AC-19, 716–723.
Akaike, H. (1978) A Bayesian analysis of the minimum AIC procedure. Annals of The Institute of Statistical Mathematics, 30, 9–14.
Chen, C. W. S. (1992) Bayesian analysis of bilinear time series models: a Gibbs sampling approach. Communications in Statistics — Theory and Methods, 21, 3407–3425
Davis, L. D. (1991) Handbook of Genetic Algorithm. Van Nostrand Rein-hold, New York.
Gabr, M. M. and Subba Rao, T. (1981) The estimation and prediction of subset bilinear time series models with applications. Journal of Time Series Analysis, 2, 155–168.
Goldberg, D. E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, MA.
Goldberg, D. E. and Deb, K. (1991) A comparative analysis of selection schemes used in genetic algorithms, Computers and Operations Research, 18 275–289.
Granger, C. W. J. and Andersen, A. P. (1978) An Introduction to Bilinear Time Series Models, Vandenhoeck and Ruprecht, Göttingen.
Holland, J. H. (1975) Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor.
Liu, J. and Blockwell, P. J. (1984). On the general bilinear time series models. J. Appl. Prob., 25, 553–64.
Ljung, G. M. and Box, G. E. P. (1978) On a measure of lack of fit in time series models, Biometrika, 65, 297–303.
Schwartz, G. (1978) Estimating the dimension of a model, The Annals of Statistics, 6, 461–464.
Subba Rao, T. (1981) On the theory of bilinear time series models, Journal of the Royal Statistical Society, Ser. B, 43, 244–255.
Subba Rao, T. and Gabr, M. M. (1984) An Introduction to Bispecral Analysis and Bilinear Time Series Models. Springer-Verlag, New York.
Syswerda, G. (1989) Uniform Crossover in Genetic Algorithms, Proceedings of the Third International Conference on Genetic Algorithms
Wei, W. W. S. (1990) Time Series Analysis: Univariate and Multivariate Methods, Addison-Wesley, MA.
Whitley (1994) A genetic algorithm tutorial. Statistics and Computing, 4, 63–85.
Wu, B. and Shih, N.-H. (1992) On the identification problem for bilinear time series models. Journal of Statistical Computation and Simulation, 43, 129–161.
Acknowledgments
The authors would like to thank the anonymous referee for comments and suggestions which greatly improved this paper. This research is supported by grants (NSC 87-2118-M-035-004, NSC 88-2118-M-035-001) from National Science Council of Taiwan for which Chen, C.W.S. and Cherng, T.-H. are grateful.
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Chen, C.W.S., Cherng, TH. & Wu, B. On the Selection of Subset Bilinear Time Series Models: a Genetic Algorithm Approach. Computational Statistics 16, 505–517 (2001). https://doi.org/10.1007/s180-001-8327-9
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DOI: https://doi.org/10.1007/s180-001-8327-9