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.