Implement multi-step-ahead forecasting with multi-point association fuzzy logical relationship for time series

Abstract

In the existing high-order fuzzy logical relationship (FLR) based forecasting model, each FLR is used to describe the association between multiple premise observations and a consequent observation. Therefore, these FLRs concentrate on the one-step-ahead forecasting. In real applications, there exist another kind of association: the association between multiple premise observations and multiple consequent observations. For such association, the existing FLRs can’t express and ignored. To depict it, the high-order multi-point association FLR is raised in this study. The antecedent and consequent of a high-order multi-point association FLR are consisted of multiple observations. Thus, the proposed FLR reflects the influence of multiple premise observations on the multiple consequent observations, and can be applied for multi-step-ahead forecasting with no cumulative errors. On the basis of high-order multi-point association FLR, the high-order multi-point trend association FLR is constructed, it describes the trend association in time series. By using these two new kinds of FLRs, a fuzzy time series based multi-step-ahead forecasting model is established. In this model, the multi-point (trend) association FLRs effective in capturing the associations of time series and improving forecasting accuracy. The benefits of the proposed FLRs and the superior performance of the established forecasting model are demonstrated through the experimental analysis.