Modelado estructural no lineal de series temporales
Palabras clave:
Modelos de Series Temporales, Modelos Estructurales Estáticos, Redes Neuronales Artificiales, Modelos Híbridos (es)Time Series Models, Structural Static Models, Artificial Neural Networks, Hybrid Models (en)
Descargas
Los modelos estructurales son herramientas conceptualmente útiles en el modelado de series temporales, toda vez que permiten la representación individual de cada componente estructural de la serie estudiada; sin embargo, la dificultad que estos presentan para representar relaciones no lineales ha desestimado su utilización en series reales. Alternativamente, los modelos basados en redes neuronales artificiales (RNA) son una alternativa promisoria para el modelado de series con características no lineales; no obstante, su incapacidad para dar una explicación económica de los parámetros calculados, hace que estas sean vistas como cajas negras. En este estudio, se propone una metodología híbrida que combina las bondades del modelado estructural en la representación explícita de las características de la serie y de las redes neuronales en la captura de relaciones no lineales. Los resultados experimentales con series reales indican que la combinación de modelos de éste tipo puede ser una vía más efectiva para el modelado de series temporales no lineales que los modelos usados individualmente.
Structural models are tools conceptually useful in time series modeling, because they allow the individual interpretation behavior of each structural component in the series; however, the difficult in the representation of nonlinear relationships of these models, have despised their use in real scries. The Artificial Neural Networks (RNA) models are a promising alternative by the nonlinear time series modeling; nevertheless, the inabilities for to explain the parameters calculate of these models do that RNA have seen as black box. In this paper, we propose a hybrid approach that uses an explicit modeling of the structural characteristics of time series by structural models, joint with modeling of nonlinear relationships provided by neural networks. Experimental results with real series suggest the combination of this models can be an effective way to nonlinear time series modeling that the individual models.
Referencias
Box, G. y Jenkins, G. (1970), Time Series Analysis: Forecasting and Control, San Francisco.
Chatfield, C. (1988), ‘What is the ’best’ method of forecasting?’, J. Appl. Statist. 15, 19-39.
Chatfield. C. (1996), ‘Model uncertainty and forecast accuracy’, J. Forecasting 15, 495-508.
Clemen, R. (1989), ‘Combining forecasts: a review and annotated bibliography with discussion’, Int. J. Forecasting 5, 559-608.
DasGupta, B., Siegelmann, H. T. y Sontag, E. (1995), ‘On the complexity of training neural networks with continuous activation functions’, IEEE Transactions on Neural Networks 6, 6.
De Gooijer, J. y Kumar, K. (1992), ‘Some recent developments in non-linear time series modelling, testing, and forecasting’, Int. J. Forecasting 8, 135-156.
Durbin, J. y Harvey, A. (1985), The effects of seat belt legislation on road casualties in Great Britain: Report on assessment of statistical evidence, Technical report, HMSO, London.
Engle, R. (1982), ‘Autoregressive conditional heterocedasticity with estimates of the variance of united Kingdom inflations’, Econometrica 50, 987-1007.
Ginzburg, I. y Horn, D. (1994), ‘Combined neural networks for time series analysis’, Adv. Neural Inf. Process. Systems 6, 224-231.
Granger, C. (1989), ‘Combining forecasts-twenty years later’, J. Forecasting 8, 167-173.
Granger, C. y Andersen, A. (1978), An Introduction to Bilinear Time Series Models.
Granger, C. y Teräsvirta, T. (1993), Modeling Nonlinear Economic Relationships.
Harvey, A. (1989), Forecasting, Structural Time Series and the Kalman Filter.
Hornik, K.. Stinchicombe, M. y White, H. (1990), ‘Using multi-layer feedforward networks for universal approximation’, Neural Networks 3, 551-560.
Hung, M. y Denton, J. (1993), ’Training neural networks with the GRG2 nonlinear optimizer', Eur. J. Oper. Res. 69, 83-91.
Kaastra, I. y Boyd, M. (1996), ‘Designing a neural network for forecasting financial and economic series’, Neurocomputing 10, 215-236.
Krogh, A. y Vedelsby, J. (1995), ‘Neural network ensembles, cross validation, and active learning’, Adv. Neural Inf. Process. 7, 231-238.
Luxhoj, J., Riis, J. y Stensballe, B. (1996), ‘A hybrid econometric-neural network modeling approach for sales forecasting’, Int. J. Prod. Econ. 43, 175-192.
Makridakis, S. (1989), ‘Why combining works?’, Int. J. Forecasting 5, 601-603.
Makridakis, S., Anderson, A., Carbone, R., Fildes, R., Hibdon, M., Lewandowski, R., Newton, J., Parzen, E. y Winkler, R. (1982), ‘The accuracy of extrapolation (time series) methods: results of a forecasting competition’, J. Foretasting 1. 111—153.
Makridakis, S., Chatfield, C., Hibon. M., Lawrence, M., Millers, T., Ord, K. y Simmons, L. (1993), ‘The M-2 competition: a real-life judgmentally based forecasting study’, Int. J. Forecasting 9. 5-29.
Masters, T. (1995), Neural, Novel and Hybrid Algorithms for Time Series Prediction.
Mehra, P. y Benjamin, W. (1997), Artificial Neural Networks: Concepts and Theory.
Newbold, P. y Granger, C. (1974). ‘Experience with forecasting univariate time series and the combination of forecasts (with discussion)’, J. R. Statist. Soc. 137, 131-164.
Palm, F. y Zellner, A. (1992), ‘To combine or not to combine? issues of combining forecasts’, J. Forecasting 11, 687- 701.
Pelikan, E., De Groot, C. y Wurtz, D. (1992), ‘Power consumption in west-bohemia: improved forecasts with decorrelating connectionist networks’, Neural Network World 2, 701-712.
Peretto, P. (1992), An Introduction to the Modeling of Neural Networks.
Perrone, M. y Cooper, L. (1993), Neural Networks for Speerhand Image Processing, Chapman & Hall, London, chapter When networks disagree: ensemble method for hybrid neural networks, pp. 126-142.
Pole, A., West, M. y Harrison, J. (1994), Applied Bayesian Forecasting and Time Series Analysis, NY.
Subramanian, V. y Hung, M. (1993), ‘A GRG2-based system for training neural networks: design and computational experience’, ORSA J. Comput. 5, 386-394.
Tong, H. (1990), Non-linear Time Series: A Dynamical System Approach, Oxford Statistical Science Series.
Velasquez, J. (2003), Construcción de Escenarios de Pronóstico del Precio de Electricidad en Mercados de Corto Plazo, Propuesta de tesis doctoral, Facultad de Minas, Universidad Nacional de Colombia.
Wedding H, D. y Cios, K. (1996), ‘Time series forecasting by combining rbf networks, certainty factors, and the box-jenkins model', Neurocomputing 10, 149-168.
Winkler, R. (1989), ‘Combining forecasts: a philosophical basis and some current issues’, Int. J. Forecasting 5. 605-609.
Zhang, G. (2003), ‘Time series forecasting using a hybrid ARIMA and neural network model’, Neurocomputing 50, 159-175.
Zhang, G., Patuwo, E. y M.Y. Hu, M. (1998), ‘Forecasting with artificial neural networks: the state of the art', Int. J. Forecasting 14, 35-62.