A novel intelligent approach for state space evolving forecasting of seasonal time series

This paper proposes a new methodology for modelling based on an evolving Neuro-Fuzzy Takagi-Sugeno (NF-TS) network used for seasonal time series forecasting. The NF-TS considers the unobservable components extracted from the time series data to evolve, that is, to adapt and to adjust its structure, where the fuzzy rules number of this network can increase or decrease according to components behaviour. The method used to extract these components is a recursive version, proposed in this paper, based on the Spectral Singular Analysis (SSA) technique. The NF-TS network adopts the principle divide to conquer, where it divides a complex problem into subproblems easier to deal, forecasting separately each unobservable component, because they present dynamic behaviours 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 NF-TS is performed, i.e., the NF-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 unobservable components data to NF-TS. The NF-TS was evaluated and compared with other recent and traditional techniques for seasonal time series forecasting, obtaining competitive and advantageous results in relation to other papers. This paper also presents a case study about real-time detection of anomalies based on a patient electrocardiogram data.