On the Potential of Fuzzy Rule-Based Ensemble Forecasting

Abstract

It is a well-known fact that there is no individual forecasting method that is generally for any given time series better than any other method. Thus, no matter how efficient a chosen method is, there always exists a danger that for a given time series the method is highly inappropriate. To overcome such a problem and avoid the danger of choosing an inaccurate method, distinct ensemble techniques that combine more individual forecasting methods are designed. These techniques construct a forecast as a (linear) combination, i.e. a weighted average, of forecasts by individual methods. It is important to stress that even very sophisticated approaches to determine appropriate weights often fail to outperform so called equal weights approach, i.e. a simple arithmetic mean of individual forecasts.

This contribution attempts to construct a novel ensemble technique that determines the weights based on time series features such as trend, seasonality, kurtosis or stationarity. The knowledge how to determine weights comes from the regression analysis. However, in order to capture the desirable issues of robustness and mainly of interpretability, the knowledge how to combine individual methods is encoded in a linguistic description, i.e. in a specific fuzzy rule base that uses linguistic evaluative expressions. Thus, the mechanism of determination of particular weights is perception-based logical deduction – a unique fuzzy inference technique that is designed for linguistic descriptions. An exhaustive experimental justification is provided in order to confirm the promising potential of the given direction of research. The suggested ensemble approach based on fuzzy rules demonstrates both, lower forecasting error and higher robustness in comparison to individual methods as well as to the equal weights ensemble.