Time series; ARIMA; Fuzzy transform; Evaluative linguistic expressions; Fuzzy natural logic

In this paper, we address non-statistical methods for forecasting and detection of structural breaks in time series. Our methods are based on the application of the unique fuzzy modeling method called fuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). The latter provides a formal model of the semantics of a part of natural language and methods for reasoning based on it. Using F-transform, we first estimate the trend-cycle. Then, using methods of FNL, we extract a sort of expert information that enables us to forecast the trend-cycle. Since F-transform also makes it possible to estimate the slope of time series over an imprecisely specified area (ignoring its volatility), we identify structural breaks through evaluation of changes in the slope by a suitable evaluative linguistic expression. We will demonstrate the effectiveness of our methods on several real time series and compare our results of forecasting with the classical ARIMA statistical method. Our methods are computationally very effective.