含非参数趋势的残差MA模型的预测方法
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摘要
为了探寻具有非参数趋势的残差移动平均模型的较为合适的预测方法,考虑了基于多项式样条的三种方法:非外推法、线性外推法和非线性外推法.模拟结果表明,线性外推法和非线性外推法拟合的均方误差(MSE)和平均绝对误差(MAE)相等且最小,线性外推法预测的MSE和MAE最小.此外,还对分行业增加值构成-金融业增加值进行了拟合和预测的实证分析,得到了与模拟算例相似的结果.这说明线性外推法是一种较好的预测方法.
In order to find a more appropriate prediction method for residual moving average models with nonparametric trend, three prediction methods based on polynomial spline are considered, non-extrapolation method, linear extrapolation method and nonlinear extrapolation method. The simulation results show that the mean squared error(MSE) and mean absolute error(MAE) of linear extrapolation method and nonlinear extrapolation method are equal and minimum, and MSE and MAE predicted by the linear extrapolation method are the smallest. Moreover, an empirical analysis is carried on the composition of industry added value--financial industry added value. The results are similar to those of simulation example. This shows that the linear extrapolation method is better.
In order to find a more appropriate prediction method for residual moving average models with nonparametric trend, three prediction methods based on polynomial spline are considered, non-extrapolation method, linear extrapolation method and nonlinear extrapolation method. The simulation results show that the mean squared error(MSE) and mean absolute error(MAE) of linear extrapolation method and nonlinear extrapolation method are equal and minimum, and MSE and MAE predicted by the linear extrapolation method are the smallest. Moreover, an empirical analysis is carried on the composition of industry added value--financial industry added value. The results are similar to those of simulation example. This shows that the linear extrapolation method is better.
引文
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[2] Burman P.Regression function estimation from dependent observations [J].Journal of Multivariate Analysis,1991,36 (2):263-279.
[3] Wu Xinqian,Yang Wancai.Spline estimate of nonlinear trend for time series[C].Proceedings - 2010 First ACIS International Symposium on Cryptography,and Network Security,Data Mining and Knowledge Discovery,E-Commerce and Its Applications,and Embedded Systems,CDEE 2010,Qinhuangdao,Hebei,China.IEEE Inc,95-98.
[4] 武新乾.线性过程误差下回归函数的样条估计[J].河南科技大学学报,2010,31(5):94-97.
[5] 叶阿忠.非参数和半参数计量经济模型理论[M].北京:科学出版社,2008.
[6] 刘锋,王鹏飞,谭祥勇,等.基于非参数自回归模型的黄金价格短期分析预测[J].数理统计与管理,2018,37(2):357-361.
[7] 戴秀菊,舒志彪.基于非参数核回归模型的隐含波动率预测[J].福州大学学报:自然科学版,2018,46 (2):156-162.
[8] 赵秀丽,赵俊龙.基于样条函数的时间序列预测模型[J].统计与决策,2007,(8):19-21.
[9] 武新乾,张刚.具有非参数趋势的残差自回归模型的预测方法[J].统计与决策,2016,(15):84-86.
[10] 武新乾,程芳.固定设计异方差非参数回归模型的预测方法[J].统计与决策,2017,(17):76-79.
[11] 王燕.应用时间序列分析[M].3版.北京:中国人民大学出版社,2014.
[12] 王振龙.应用时间序列分析[M].北京:中国统计出版社,2000.