Filtering out high frequencies in time series using F-transform

In this paper, we focus on application of fuzzy transform (F-transform) to analysis of time series under the assumption that the latter can be additively decomposed into trend-cycle, seasonal component and noise. We prove that when setting properly width of the basic functions, the inverse F-transform of the time series closely approximates its trend-cycle. This means that the F-transform almost completely removes the seasonal component and noise. The obtained theoretical results are demonstrated on two artificial time series whose trend cycle is precisely known and on three real time series. At the same time, comparison with three classical methods, namely STL-method, SSA-method and low pass Butterworth filter is also provided.