Neuro-fuzzy system for chaotic time series forecasting

We report on an on-going study to assess potential benefits using soft computing methods in forecasting problems. Our goal is to forecast natural phenomena represented by time series that show chaotic features. We use a neuro-fuzzy system for its ability to adapt to numerical data and for the possibility to input and extract expert knowledge expressed in words. We present results of experiments designed to study how to shape a neuro-fuzzy systems to forecast chaotic time series. Our main conclusions are: (1) The neuro-fuzzy system is able to forecast a synthetic chaotic time series with high accuracy if the number of inputs and the time delay between them are chosen adequately. (2) The Takens-Mane theorem from chaos theory gives a useful lower bound on the minimal number of inputs. (3) The time delay between the inputs can not be set a priori. It has to be tuned for every different times series. (4) The number of fuzzy rules seems related to the size of the learning set and not to the structure of the chaotic dynamical system. We tentatively try to interpret the rules that the neuro-fuzzy system has learned. Finally we discuss the adequacy of the whole set of fuzzy rules to forecast locally the dynamical system.