Deterministic vector long-term forecasting for fuzzy time series

In the last decade, fuzzy time series have received more attention due their ability to deal with the vagueness and incompleteness inherent in time series data. Although various improvements, such as high-order models, have been developed to enhance the forecasting performance of fuzzy time series, their forecasting capability is mostly limited to short-term time spans and the forecasting of a single future value in one step. This paper presents a new method to overcome this shortcoming, called deterministic vector long-term forecasting (DVL). The proposed method, built on the basis of our previous deterministic forecasting method that does not require the overhead of determining the order number, as in other high-order models, utilizes a vector quantization technique to support forecasting if there are no matching historical patterns, which is usually the case with long-term forecasting. The vector forecasting method is further realized by seamlessly integrating it with the sliding window scheme. Finally, the forecasting effectiveness and stability of DVL are validated and compared by performing Monte Carlo simulations on real-world data sets.