Synergizing Two Types of Fuzzy Information Granules for Accurate and Interpretable Multistep Forecasting of Time Series

High accuracy and decent interpretability are two main pursuits in time series multistep forecasting. Trend fuzzy information granulation shows the potential to improve accuracy. That is, trend fuzzy information granulation-based models give multistep forecasts by predicting a trend-type fuzzy information granule (FIG) at one time, thus avoiding cumulative errors resulting from repetitive iterations. However, since trend fuzzy information granulation focuses on trend information but misses magnitude information of time series, the models based on which are decently interpretable in the sense of trend but not magnitude, leading to the accuracy-interpretability dilemma. To overcome this dilemma, we first propose a new type of FIGs, named multiamplitude FIG, to interpret amplitude features and magnitude distributions. Then we present trend-magnitude synergy-oriented fuzzy information granulation, which constructs two types of FIGs on each segment simultaneously: multilinear-trend FIG and multiamplitude FIG. They, respectively, act as trend and magnitude semantic descriptors of time series. Such fuzzy information granulation method benefits to mining multilinear-trend and multiamplitude fuzzy rules that can effectively interpret complex trend associations and magnitude associations. With such new fuzzy rules, we synergize trends and magnitudes well to develop a time series multistep forecasting model. This model operates at the granular level, predicting a multilinear-trend FIG and a multiamplitude FIG at one time. Therefore, it is with not only high accuracy but also decent interpretability thanks to the sound trend-magnitude synergy. Experiments verify the validity of our multistep forecasting model in accuracy and interpretability.