High-order difference heuristic model of fuzzy time series based on particle swarm optimization and information entropy for stock markets

The forecasting problem of time series is an intriguing and pivotal research topic. Due to salient capabilities of tracking uncertainty and vagueness in observations, fuzzy time series has received more and more attention from not only researchers but investors. However, there exist two unsolved problems in the modeling of fuzzy time series, i.e., how to partition the universe of discourse and how to construct fuzzy logic relationships effectively. Here we introduced the technique of particle swarm optimization (PSO) to partition the universe of discourse, and combine information entropy to define the fuzzy sets. Based on these two algorithms, a novel model of fuzzy time series is proposed. To testify model's validity, the authors forecasted the enrollments and Dow index. The empirical results demonstrate that the presented method has higher forecasting accuracy rates than the excising ones.