论文标题
在连续时间灰色型号的统一框架上：一个积分匹配的视角
On unified framework for continuous-time grey models: an integral matching perspective
论文作者
论文摘要
由于有关灰色预测模型的大多数研究都集中在开发新型模型和提高准确性上，因此对各种模型之间的建模机制和关系的关注相对有限。本文旨在统一和重建连续的灰色模型，突出不同模型之间的差异和相似性。首先，提出了统一的灰色模型形式，并将其简化为降低的普通微分方程。然后，提出了由积分转换和最小二乘组成的积分匹配，以同时估计结构参数和初始值。累积总和运算符是灰色建模中的重要元素，被证明是积分转换公式的离散近似。接下来，通过基于积分匹配的普通微分方程重建灰色模型。最后，通过广泛的仿真研究将现有的灰色模型与重建模型进行了比较，一个现实世界的示例显示了如何应用和进一步验证重建的模型。
Since most of the research about grey forecasting models is focused on developing novel models and improving accuracy, relatively limited attention has been paid to the modelling mechanism and relationships among diverse kinds of models. This paper aims to unify and reconstruct continuous-time grey models, highlighting the differences and similarities among different models. First, the unified form of grey models is proposed and simplified into a reduced-order ordinary differential equation. Then, the integral matching that consists of integral transformation and least squares, is proposed to estimate the structural parameter and initial value simultaneously. The cumulative sum operator, an essential element in grey modelling, proves to be the discrete approximation of the integral transformation formula. Next, grey models are reconstructed by the integral matching-based ordinary differential equations. Finally, the existing grey models are compared with the reconstructed models through extensive simulation studies, and a real-world example shows how to apply and further verify the reconstructed model.
