Evolving Methodology in Unobservable Components Space for Multivariate Time Series Forecasting

Abstract

This paper presents an evolving Takagi-Sugeno neuro-fuzzy network that modify its fuzzy rule structure to forecast multivariate time series. This neuro-fuzzy network considers as input data the unobservable components extracted from the time series using the MR-SSA method, proposed in this paper. An evolving clustering algorithm based on eClustering+ was used to formulate antecedent propositions of fuzzy rules, where the number of rule can increase or decrease. Due to the use of these components, the data space considered by evolving clustering algorithm is called unobservable components space in this paper. Therefore, the proposed multivariate method is trained to perform the forecast of each component separately and, finally, to obtain the forecasting of the time series considered. The consequents propositions of fuzzy rules are linear models in state space, where the states correspond to the unobservable components themselves. The experiments considered 3 real case studies, highlighting its application, importance in decision making by time series experts and proposing them as a benchmark for multivariate evolving time series forecasting methods.