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Since most of the research about grey forecasting models is focused ondeveloping novel models and improving accuracy, relatively limited attentionhas been paid to the modelling mechanism and relationships among diverse kindsof models. This paper aims to unify and reconstruct continuous-time greymodels, highlighting the differences and similarities among different models.First, the unified form of grey models is proposed and simplified into areduced-order ordinary differential equation. Then, the integral matching thatconsists of integral transformation and least squares, is proposed to estimatethe structural parameter and initial value simultaneously. The cumulative sumoperator, an essential element in grey modelling, proves to be the discreteapproximation of the integral transformation formula. Next, grey models arereconstructed by the integral matching-based ordinary differential equations.Finally, the existing grey models are compared with the reconstructed modelsthrough extensive simulation studies, and a real-world example shows how toapply and further verify the reconstructed model.

On unified framework for continuous-time grey models: an integral matching perspective