How the GM(1,N) Grey Model Predicts Multi‑Variable Systems
The GM(1,N) prediction model extends the classic GM(1,1) approach to multiple indicator variables by applying accumulated generating operations, forming a first‑order differential equation, converting it to a discrete model, and using least‑squares estimation to derive prediction values for each variable.
GM(1,N) Prediction Model
Assume the system has N indicator variables, each with its own reference sequence.
By performing accumulated generating operations, an accumulated generating series is obtained.
The resulting first‑order differential equation with one variable can be expressed in a standard form.
Transforming the equation into a discrete model yields a second‑order accurate numerical model.
Let the model parameters be estimated by the least‑squares method; the resulting estimates provide the predicted values for each variable when the model is restored to the original scale.
Reference
司守奎，孙玺菁 Python数学实验与建模
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