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Statistical Methods for Fuzzy Data by Reinhard Viertl

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24

Descriptive methods for fuzzy time series

Descriptive methods of time series analysis work without stochastic models. The goal of these methods is to find trends and seasonal influence in time series by elementary methods. A short survey of such methods for standard time series is given in Janacek (2001).

A fuzzy time series (xt*)tT is an ordered sequence of fuzzy numbers, where usually T = {1, 2, …, N}. Formally a one-dimensional fuzzy time series is a mapping T which gives for any time point t a fuzzy number xt*. Classical time series are special forms of fuzzy time series.

A reasonable generalization should generate the classical results in the case of classical data. This is guaranteed if the extension principle is used.

For the approximation by a polynomial trend in the case of fuzzy time series see Körner (1997a), Körner and Näther (1998), Munk (1998), Näther and Albrecht (1990).

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