Grey theory-based time series models are widely used in various fields and disciplines. While most of the research is focused on the development and improvement of novel discrete-time models, very limited attention has been paid to the relationships among diverse models. The current paper proposes a methodological and practical framework to unify the single-variable, multi-variable, and multi-output discrete-time grey models, making it easier for practitioners to select an appropriate model for a given time-series forecasting problem. The recursive extrapolation strategy is present to generate multi-step ahead forecasts and four model families are deduced within the universal framework. Large-scale simulation studies are conducted to evaluate the finite-sample fitting and multi-step ahead forecasting performance. The proposed approach is illustrated using application examples from the indirect measurement of the tensile strength of materials.

基于灰色理论的时间序列模型已广泛应用于各个领域和学科。尽管大多数研究都集中在新颖离散时间模型的开发和改进上，但对各种模型之间的关系的关注却非常有限。本文提出了一种方法和实践框架，以统一单变量，多变量和多输出离散时间灰色模型，从而使从业者更容易为给定的时间序列预测问题选择合适的模型。存在递归外推策略以生成多步提前预测，并且在通用框架内推导了四个模型族。进行了大规模仿真研究，以评估有限样本拟合和多步提前预测性能。