A Combination of Fuzzy Techniques and Chow Test to Detect Structural Breaks in Time Series

Abstract

In a series of papers, we suggested a non-statistical method for the detection of structural breaks in a time series. It is based on the applications of special fuzzy modeling methods, namely Fuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). In this paper, we combine our method with the principles of the classical Chow test, which is a well-known statistical method for testing the presence of a structural break. The idea is to construct testing statistics similar to that of the Chow test which is formed from components of the first-degree F-transform. These components contain an estimation of the average values of the tangents (slopes) of the time series over an imprecisely specified time interval. In this paper, we illustrate our method and its statistical test on a real-time series and compare it with three classical statistical methods.