TREND-CYCLE ESTIMATION USING FUZZY TRANSFORM OF HIGHER DEGREE

In this paper, we provide theoretical justication for the appli- cation of higher degree fuzzy transform in time series analysis. Under the assumption that a time series can be additively decomposed into a trend- cycle, a seasonal component and a random noise, we demonstrate that the higher degree fuzzy transform technique can be used for the estimation of the trend-cycle, which is one of the basic tasks in time series analysis. We prove that high frequencies appearing in the seasonal component can be arbitrarily suppressed and that random noise, as a stationary process, can be success- fully decreased using the fuzzy transform of higher degree with a reasonable adjustment of parameters of a generalized uniform fuzzy partition.