Metodologia de modelagem computacional inteligente para previsão de séries temporais baseada em sistemas evolutivos e análise espectral singular recursiva

Abstract

This thesis proposes an evolving methodology for univariate or multivariate time series fore casting based on neuro-fuzzy network structure, updating its knowledge base for each new observation. This proposal has a hybrid characteristic, considering a neuro-fuzzy network whose consequents of fuzzy rules contain vector autoregression models. These models are composed by unobservable components, i. e., hidden patterns extracted from the time series. To extract these components, a recursive and parallel version of the Singular Spectrum Analysis (SSA) method is proposed in the paper. This version is named Parallel Recursive Singular Spectrum Analysis (PRSSA), and the parallel name is used because, for each time series, there is an asso ciated decomposition procedure. Unifying these methods, the proposed methodology is called PRSSA+ENFN (Parallel Recursive Singular Spectrum Analysis and Evolving Neuro-Fuzzy Network), highlighting its hybrid profile again. Hence, the PRSSA+ENFN method proposed applies the "divide to conquer" idea, i.e., it extracts the unobservable components and forecasts them separately using the neuro-fuzzy network, because these components has less complex behavior than the complete time series. After components forecasting, these results are grouped together to predict the original time series. Furthermore, the neuro-fuzzy network has an evolv ing characteristic, i.e., it considers the dynamic behavior of these components to evolve its structure for each new observation, where the number of fuzzy rules can increase or decrease according to this dynamic. The flexibility of the PRSSA+ENFN method with both univariate or multivariate time series was evaluated on the experimental results, considering the recurrent or direct type of forecasting. In addition, the proposed approach was compared with other studies and methods used in literature for time series forecasting, showing competitive results and the developed methodology can be used in cases involving complex and non-stationary time series. The PRSSA+ENFN was applied to a real problem related to the Covid-19 pandemic in Maranhão - Brazil, evaluating its behavior to forecast the daily numbers of cases and deaths caused by this disease. Then, this proposed method proved to be a potential approach to assist specialists in the decision-making process and to be explored in future works.