A Combination of Fuzzy Techniques and Chow Test to DetectStructural Breaks in Time Series
In a series of papers, we suggested a non-statistical method for the detection of structuralbreaks in a time series. It is based on the applications of special fuzzy modeling methods, namelyFuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). In this paper, wecombine our method with the principles of the classical Chow test, which is a well-known statisticalmethod for testing the presence of a structural break. The idea is to construct testing statistics similarto that of the Chow test which is formed from components of the first-degree F-transform. Thesecomponents contain an estimation of the average values of the tangents (slopes) of the time seriesover an imprecisely specified time interval. In this paper, we illustrate our method and its statisticaltest on a real-time series and compare it with three classical statistical methods.