Abstract
In this paper, we provide theoretical justification for the application 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 successfully decreased using the fuzzy transform of higher degree with a reasonable adjustment of parameters of a generalized uniform fuzzy partition.
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