Integrate new cross association fuzzy logical relationships to multi-factor high-order forecasting model of time series

In any multi-factor high-order fuzzy logical relationship (FLR) based forecasting model, a FLR reflects the influence of both the main factor (the forecasted factor) and all the influence factors on the main factor. Thus, the antecedent of a FLR includes multiple premises related to the main factor as well as all the influence factors. In real time series, there may exist another kind of influence: the cross association influence which is from a part of influence factor(s) on the main factor. To describe such kind of influence, we propose the concept of multi-factor high-order cross association FLRs (CAFLRs). The antecedent of a CAFLR includes some premises related to a part of influence factors. The proposed CAFLRs are divided into two categories: short-cross association FLRs and long-cross association FLRs, which describe the influence on the consequent observation from the premise observations at the closest consecutive moments and the premise observations at the non-closest non-consecutive moments respectively. Based on the concept of CAFLRs, a novel forecasting model is built up. In the proposed model, more FLRs than in the existing models can be mined from historical observations and added to the rule base, which further improve the prediction accuracy by raising the possibility of finding available forecasting FLRs. Superior performance of the proposed model has been verified in the experiments by comparing with Nonlinear Autoregressive Neural Networks, Autoregressive Model, Support Vector Regression and some other FLR based forecasting models.