fuzzy transform; high frequency; seasonal component; time series

In this paper, we provide a theoretical justification for the application of the higher degree fuzzy transform in time series analysis. We demonstrate that the higher degree fuzzy transform technique can be used for the suppression of high frequencies in time series, which belongs among the essential assumptions for a successful extraction of the trend (trend-cycle) of time series. More precisely, if a time series can be additively decomposed into a trend-cycle, a seasonal component and a noise, we show that high frequencies appearing in the seasonal component can be arbitrarily suppressed using the fuzzy transform of higher degree with a reasonable adjustment of parameters of a generalized uniform fuzzy partition.