A New Approach for Enhancing Forecaster Performance for Chaotic Time Series

In this paper, we present a new chaotic control algorithm that leads to a fairly substantial improvement in the performance of the traditional fuzzy chaotic time series forecaster. The main idea is to use the Fuzzy Basis Functions (FBFs) expansion which allows us to view a Fuzzy Logic System (FLS) as a linear combination of the consequent parameters. Hence, the possibility to use a linear optimization to tune these parameters, which results in a two-stage algorithm. The first step consists in extracting the training data from a chaotic system with different initial conditions, and the second one consists on applying the generalized orthogonality principle, in order to construct a globally more efficient FLS forecaster. Such a forecaster yields the ability to produce substantially improved results when applied to predict the output of the Mackey-Glass time series.