As one type of time series, interval-valued time series (ITS) is encountered frequently in many fields such as finance, environment, agriculture and so on since it can describe the uncertainty and variability of observed variables. The modeling of ITS is an ongoing issue pursued by researchers. In this paper, a novel rule-based granular ITS model is proposed by considering the interval-valued data as interval information granules in the framework of granular computing (GrC). The development of the proposed granular model consists of three components with progressive relationship, that is, the generation of granular prototypes, the formation of initial granular model and the refinement of the initial granular model. Further, the detail computation of reasoning of the corresponding granular model is also given. The resulting granular models have not only interpretability but also an ability to process ITS containing linguistic variables. Numerical experiments on six financial datasets and two meteorological datasets from real world reveal the impact of the parameter involved in the proposed method on the resulting granular model, and also exhibit that the resulting granular model is superior to seven existing competitive models including interval Holt one, multi-output support vector regression one and interval arithmetic-based multilayer perceptron one etc.

作为时间序列的一种，区间值时间序列（ITS）可以描述观测变量的不确定性和可变性，因此在金融、环境、农业等许多领域中经常遇到。ITS 的建模是研究人员一直在追寻的问题。本文在粒计算(GrC)框架下，将区间值数据视为区间信息粒，提出了一种新的基于规则的粒状ITS模型。所提出的粒模型的开发由三个具有递进关系的组件组成，即粒原型的生成、初始粒模型的形成和初始粒模型的细化。此外，还给出了相应粒模型推理的详细计算。由此产生的粒度模型不仅具有可解释性，而且还具有处理包含语言变量的 ITS 的能力。对来自现实世界的六个金融数据集和两个气象数据集的数值实验揭示了所提出方法所涉及的参数对所得粒状模型的影响，并表明所得粒状模型优于包括区间霍尔特一号在内的七个现有竞争模型，多输出支持向量回归一和基于区间算法的多层感知器一等。