SUPPRESSION HIGH FREQUENCIES IN TIME SERIES USING FUZZY TRANSFORM OF HIGHER DEGREE

In this contribution, we provide a theoretical justification for the application of the higher degree fuzzy transform in time series analysis. We show that the higher degree fuzzy transform technique suppresses high frequencies in time series, which is one of the important assumptions in a successful extraction of the trend-cycle of time series. More precisely, assuming that a time series can be additively decomposed into a trend (trend-cycle), a seasonal component and a noise, we demonstrate that high frequencies, which appear in the seasonal component, can be arbitrarily suppressed using the fuzzy transform of higher degree provided that a reasonable setting of a generalized uniform fuzzy partition is considered.