Automated Linear Modeling of Time Series with Self Adaptive Genetic Algorithms

Two heuristic algorithms that automatically calculate linear expressions for time series (TS) are presented. The algorithms are based on the Box-Jenkins methodology in order to estimate the maximum number of terms of the linear expression and the intervals in which the series coefficients vary. With this information and establishing beforehand the number of terms that are required by the user, self adaptive genetic algorithms (SAGA) are applied in several stages of optimization to obtain the series model. It is worth to mention that these algorithms allow treating series with time-dependent trends and variance. In the paper the results of the application of SAGA to the NN3-reduced TS are also presented concluding that six of the eleven examples can be considered linear series. Regardless of the existence of papers where genetic algorithms are used in TS, it is important to mention that no reference of the use of SAGA in the area was found.

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

[2]  David E. Goldberg,et al.  Genetic Algorithms, Tournament Selection, and the Effects of Noise , 1995, Complex Syst..

[3]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[4]  Carlo Gaetan,et al.  Subset ARMA Model Identification Using Genetic Algorithms , 2000 .

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

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

[7]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[8]  José Neves,et al.  Evolving Time Series Forecasting ARMA Models , 2004, J. Heuristics.

[9]  Marcelo C. Medeiros,et al.  A flexible coefficient smooth transition time series model , 2005, IEEE Transactions on Neural Networks.

[10]  Marcelo C. Medeiros,et al.  A hybrid linear-neural model for time series forecasting , 2000, IEEE Trans. Neural Networks Learn. Syst..

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

[12]  Steven C. Wheelwright,et al.  Forecasting methods and applications. , 1979 .

[13]  Thomas Bck,et al.  Self-adaptation in genetic algorithms , 1991 .

[14]  James B. McDonald,et al.  Time Series Prediction With Genetic‐Algorithm Designed Neural Networks: An Empirical Comparison With Modern Statistical Models , 1999, Comput. Intell..

[15]  Marco A. H. Reyes,et al.  Dinámica de procesos biológicos no covalentes a nivel molecular , 2000 .

[16]  M. Pérez-Tello,et al.  Mass balance calculations in copper flash smelting by means of genetic algorithms , 2004 .

[17]  R. K. Dahule,et al.  Obtaining functional form for chaotic time series evolution using genetic algorithm. , 1999, Chaos.

[18]  Martin A. Tanner,et al.  Mixtures-of-experts of autoregressive time series: asymptotic normality and model specification , 2005, IEEE Transactions on Neural Networks.

[19]  George G. Szpiro.  Forecasting chaotic time series with genetic algorithms , 1997 .

[20]  Thomas Bäck,et al.  The Interaction of Mutation Rate, Selection, and Self-Adaptation Within a Genetic Algorithm , 1992, PPSN.

[21]  Ramón Garduño-Juárez,et al.  About singularities at the global minimum of empiric force fields for peptides , 2001 .