Filtering out high frequencies in time series using F-transform with respect to raised cosine generalized uniform fuzzy partition

In this paper, we apply the F-transform technique with respect to raised cosine generalized uniform fuzzy partition to analysis of time series. We assume that the time series can be additively decomposed into trend-cycle, seasonal component and noise. We will prove that when constructing reasonably the fuzzy partition then the inverse F-transform of the time series provides a good approximation of its trend-cycle. Namely, the F-transform with respect to raised cosine generalized uniform fuzzy partition is able to eliminate completely the seasonal component and significantly reduce noise.