Time series modeling based on fuzzy transform

It is well known that smoothing is applied to better see patterns and underlying trends in time series. In fact, to smooth a data set means to create an approximating function that attempts to capture important features in the data, while leaving out noises. In this paper we choose, as an approximation function, the inverse fuzzy transform (introduced by Perfilieva in Fuzzy Sets Syst 157:993–1023, 2006 [3]) that is based on fuzzy partitioning of a closed real interval into fuzzy subsets. The empirical distribution we introduce can be characterized by its expectiles in a similar way as it is characterized by quantiles. © Springer International Publishing Switzerland 2017