基于Cramer法则的区间灰数预测模型参数优化方法研究

Research on the Parameter Optimal Method of Interval Grey Number Prediction Model based on Cramer Rule

以改善区间灰数预测模型的模拟及预测性能为目的,对区间灰数预测模型的参数优化方法进行研究,应用Cramer法则推导了核序列GM(1,1)模型通用形式的参数无偏估计新方法,从理论上证明了新方法对非齐次指数"核"序列的模拟无偏性,并在此基础上构建了一种新的区间灰数预测模型;通过与优化前的区间灰数预测模型模拟精度进行比较,结果表明新模型具有更为优秀的模拟及预测性能。此研究成果对丰富和完善灰色预测模型方法体系与拓展灰色模型应用范围,具有积极意义。

The parameter optimal method of interval grey number prediction model was studied to improve its simulative and predictive performance in this paper. It applied Cramer rule to deduce the novel unbiased estimation method of GM（1,1） model common form for interval grey numbers kernel sequence, and the simulative unbiasedness of the novel method for nonhomogeneous exponent kernel sequences has been theoretically proven and a new interval grey number prediction model has been established. Comparing the simulative accuracy of the novel model with that of the previous interval grey model without parameter optimization reveals that the novel method has better performances in terms of modeling and prediction. The findings in this paper enrich the literature of grey prediction model and pave the way towards extending the application of grey model.