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Abstract
The aim of this study is to show that the integration of two soft computing techniques, namely the F-transform and fuzzy tendency modeling, can be successfully used in the analysis and forecasting of time series. The proposed method is based on the two-term additive decomposition of a time series, in which the first term is a low-frequency trend (expressed using direct F-transform components), and the second term is a residual vector that is processed as a stationary time series. A theoretical justification is given, and experiments are included. A practical application that shows the analysis of a time series with economic indicators is demonstrated.
Acknowledgments
The authors acknowledge that this paper was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and under a partial support of the projects MŠMT-7026/2012-36 (KONTAKT II, LH 12229 “Research and development of methods and means of intelligent analysis of time series for the strategic planing problems”) and RFFI-10-01-00183.
Notes
is the set of reals.
The difference between the nodes and points is that the nodes establish a grid on the set of points.
A time series with fuzzy observations is time-invariant if its fuzzy relation model does not depend on a time shift (Song and Chissom Citation1993a).
The (max–min)-composition of a fuzzy set on X and a fuzzy relation
on
is the fuzzy set
on
such that
.