TaSe Model for Long Term Time Series Forecasting Luis Javier Herrera, H´ ector Pomares, Ignacio Rojas, Alberto Gui l´ en, Olga Valenzuela, and Alberto Prieto University of Granada, Department of Computer Architecture and Technology, E.T.S. Computer Engineering, 18071 Granada, Spain http://atc.ugr.es Abstract. There exists a wide range of paradigms and a high num- ber of different methodologies applied to the problem of Time Series Prediction. Most of them are presented as a modified function approx- imation problem using I/O data, in which the input data is expanded using outputs at previous steps. Thus the model obtained normally pre- dicts the value of the series at a time (t + h) using previous time steps (t - τ1), (t - τ2),..., (t - τn). Nevertheless, learning a model for long term time series prediction might be seen as a completely different task, since it will generally use its own outputs as inputs for further training, as in recurrent networks. In this paper we present the utility of the TaSe model using the well-known Mackey Glass time series and an approach that upgrades the performance of the TaSe one-step-ahead prediction model for long term prediction. 1 Introduction There exist several methodologies and approaches to deal with time series pre- diction problems. The TaSe model, that was first presented in [3] and whose full learning methodology was fully developed in [4], is a modified TSK model [1] that uses a Grid Partitioning (thus a Grid-Based Fuzzy System GBFS [5] type) of the input space that partially overcomes the two main drawbacks of this type of models: the curse of dimensionality problem and the lack of interpretability. The curse of dimensionality problem has to do with the exponential growth in the number of rules when the number of input dimensions and the number of membership functions per input variable grow. The lack of interpretability has to do with different aspects that fuzzy models should include but that most of the times are lost in the design and in the learning process: the transparency of the model (transparent partition of the input space), the need of maintaining a relatively low number of rules [7] (very related thus with the curse of dimen- sionality problem) and, more specifically for the TSK models, the interaction of the global and local models [8] (that should allow us to interpret the rules comprising the TSK system as linearizations of the nonlinear subjacent system). The TaSe model considers these intrinsic aspects of the TSK fuzzy systems, providing high accuracy for function approximation and time series prediction J. Cabestany, A. Prieto, and D.F. Sandoval (Eds.): IWANN 2005, LNCS 3512, pp. 1027–1034, 2005. c  Springer-Verlag Berlin Heidelberg 2005 l