Análise de séries temporais fuzzy para previsão e identificação de padrões comportamentais dinâmicos

Abstract

The good results obtained by the fuzzy approaches applied in the analysis of time series (TS) has contributed significantly to the growth of the area. Although there are satisfactory results in TS analysis with methods that use the classic concepts of TS and with the recent concepts of fuzzy time series (FTS), there is a lack of models combining both areas. Face of this context, the contributions of this thesis are associated with the development of models for TS analysis combining the concepts of FTS with statistical methods aiming at the improvement in accuracy of forecasts and in identification of behavioral changes in the TS. In order to allow a suitable fuzzy representation of crisp values observed, the approaches developed in this thesis were combined with a new proposal for pre-processing of the data. The prediction value is calculated from a new smoothing technique combined with an extension of the fuzzy logic relationships. This combination allow to be considered in value computed different degrees of influence to the most recent behavior and to the oldest behavior of the series. In situations where the model does not have the necessary knowledge to calculate the predicted value, the concepts of simple linear regression are combined with the concepts of the FTS to identify the most recent trend in the TS. The approach developed for the behavioral analysis of the TS aims to identify changes in behavior from the definition of prototypes that represent the groups of the TS and from the segmentation of the series that will be analyzed. In this new approach, the dissimilarity between a segment of a TS and the corresponding interval of a given prototype is defined by metric Fuzzy Dynamic Time Warping weighted by a new smoothing technique applied to the distance matrix between the observed data. The accuracy obtained by the forecast model not only demonstrates the effectiveness of the developed approach, but also shows the evolution of model throughout the research and the importance of preprocessing in the forecast. The analysis of segmented TS identifies satisfactorily the behavioral changes of the series by calculating the membership functions of these segments in the respective groups represented by the prototypes.