Metodologia evolutiva para previsão inteligente de séries temporais sazonais baseada em espaço de estados não-observáveis

Abstract

This paper proposes a new methodology for modelling based on an evolving Neuro-Fuzzy Network Takagi-Sugeno (NFN-TS) for seasonal time series forecasting. The NFN-TS use the unobservable components extracted from the time series to evolve, i.e., to adapt and to adjust its structure, where the number of fuzzy rules of this network can increase or reduced according the components behavior. The method used to extract the components is a recursive version developed in this paper based on the Spectral Singular Analysis (SSA) technique. The proposed methodology has the principle divide to conquer, i.e., it divides a problem into easier subproblems, forecasting separately each component because they present dynamic behaviors that are simpler to forecast. The consequent propositions of fuzzy rules are linear state space models, where the states are the unobservable components data. When there are available observations from the time series, the training stage of NFN-TS is performed, i.e., the NFN-TS evolves its structure and adapts its parameters to carry out the mapping between the components data and the available sample of original time series. On the other hand, if this observation is not available, the network considers the forecasting stage, keeping its structure fixed and using the states of consequent fuzzy rules to feedback the components data to NFN-TS. The NFN-TS was evaluated and compared with other recent and traditional techniques for forecasting seasonal time series, obtaining competitive and advantageous results in relation to other papers. This paper also presents a case study of proposed methodology for real-time detection of anomalies based on a patient’s electrocardiogram data.