| 自适应灰色多项式模型 |
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| 引用本文：刘晓梅,李归澳,高美娜.自适应灰色多项式模型[J].上海第二工业大学(中文版),2025,42(1):66-77 |
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| 基金项目:国家自然科学基金(11971299) 资助 |
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| 中文摘要:灰色多项式模型(GMP(1, 1,N)) 是预测非线性“小样本” 序列的普适性方法, 其右端灰作用量为N 次多项式, 包含所有不大于N 的幂次项。而实际数据的累加序列往往只显著地呈现出部分幂次序列的特点, 这与GMP(1, 1,N) 的模型结构不符。为了更好地适应实际序列的特点, 引入了逐步回归法, 以数据为驱动, 筛选出与实际序列特点相吻合的重要幂次项, 构建了自适应灰色多项式模型(GMPS(1, 1,N))。此模型简化了原灰色多项式模型的结构, 同时提高了预测的精度。通过石家庄、衡水两个城市的城镇居民家庭人均可支配收入的实例, 说明了此模型结构简单、拟合和预测性能均优于GMP(1, 1,N) 模型、含时间幂次项灰色模型(GM(1, 1,t )), 克服了过拟合和欠拟合现象, 验证了新模型的有效性。 |
| 中文关键词:灰色预测 时间幂次项 灰色多项式模型 逐步回归 |
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| An Adaptive Grey Polynomial Model |
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| Abstract:The grey polynomial model (GMP(1, 1,N)) is generally suitable for predicting nonlinear “small-sample” sequences. For GMP((1, 1,N) model, the right grey forcing quantity is the Nth degree polynomial, containing all time power terms with a degree not exceeding N. In reality, the cumulative sequences often exhibit the characteristics of some special time power terms, which is inconsistent with GMP((1, 1,N) model. In order to match the features of actual sequences, an adaptive grey polynomial model (GMPS((1, 1,N)) is proposed by introducing the stepwise regression method, which is driven by the data to choose the important power items that are consistent with the characteristics of the actual sequence. It simplifies the structure of the grey polynomial model and improves the predicted accuracy. The examples of per capita disposable income of urban households in Shijiazhuang and Hengshui, show that the proposed model has a simpler structure and better fitting and predictive performances than GMP((1, 1,N) model and grey model with time power term (GM((1, 1,t )), and overcomes the over-fitting and underfitting phenomenon. To sum up, the results verify the validity of GMPS((1, 1,N) model. |
| keywords:grey forecast time power terms grey polynomial model stepwise regression |
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