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Optimizing GM(1,1) model based on grey derivative and prediction coefficient. (Chinese. English summary) Zbl 1313.93024

Summary: If the GM(1,1) model is applicable to nearly exponential case, a method of combining grey derivative optimization with using the simulated minimum sum of relative error square of the original sequence to estimate forecast coefficient \(c\) is proposed to construct a new optimization GM(1,1) model of simplified calculation. The prediction formula \(\hat{x}^{(0)}(k)=ce^{-ak}\) of the model is formally more concise. The strict index series is theoretically verified that parameter \(a\) has white exponential law of coincident property and prediction coefficient \(c\) has white coefficient of coincidence property.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
62M20 Inference from stochastic processes and prediction
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