Time series interval forecast using GM(1,1) and NGBM(1, 1) models

Grey forecast is used for few and uncertain data, and its forecast results have very high accuracy. Although numerous researchers have developed various grey forecasting models, the forecast results of these models are limited to single-point forecast values and cannot provide more valuable information (e.g. possible estimation range) for decision-makers. In order to address this problem, this paper proposes two grey interval forecasting methods: interval GM(1, 1) and interval NGBM(1, 1), for few and uncertain time series data. To evaluate the forecast accuracy of the two grey interval methods, this study took the short-term forecast of the passenger volume of Taiwan High Speed Rail as an example and compared the forecast accuracy of the proposed two methods with that of three current grey forecasting methods. The forecast results showed that the proposed two methods have the highest forecast accuracy among the five grey forecasting methods. The grey interval forecast value provided by the proposed methods can help decision-makers make more accurate judgement within a probable variation range.