Michal Holcapek - Institute for Research and Applications of Fuzzy Modelling, NSC IT۴Innovations, University of Ostrava, ۳۰. dubna ۲۲, ۷۰۱ ۰۳ Ostrava ۱, Czech Republic
Linh Nguyen - Institute for Research and Applications of Fuzzy Modelling, NSC IT۴Innovations, University of Ostrava, ۳۰. dubna ۲۲, ۷۰۱ ۰۳ Ostrava ۱, Czech Republic

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.

Fuzzy transform, Time series analysis, Seasonal component, Stationary process, Random noise, Trend-cycle estimation