Abstract
In this paper, we address nonstatistical 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.
The work was supported from ERDF/ESF by the project “Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region” No. CZ.02.1.01/0.0/0.0/17-049/0008414.
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Notes
- 1.
This is an experimental software developed in the Inst. for Research and Applications of Fuzzy Modeling of the University of Ostrava, Czech Republic, which implements the described method (see http://irafm.osu.cz/en/c110_lfl-forecaster/). Its author is Viktor Pavliska.
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The interval [0, 1] can be replaced by a proper bounded lattice.
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Also Box-Jenkins model.
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\(RMSE = \sqrt {\frac {1}{n}\sum \limits _{i = 1}^n {{{({y_i} - {x_i})}^2}} }\), where yi are the predicted values, xi are the actual values, and n is the number of observations.
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Truong, T.T.P., Novák, V. (2023). An Improved Forecasting and Detection of Structural Breaks in Time Series Using Fuzzy Techniques. In: Valenzuela, O., Rojas, F., Herrera, L.J., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis and Forecasting. ITISE 2021. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-14197-3_1
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