摘要
对数变换不仅能消除非平稳时间序列中的"长期趋势",还能明显降低"季节性"和"剩余的随机波动"的波动范围,从而降低预测的均方误差。但是高斯白噪声经过对数变换会形成一个小的非0数学期望,使得预测的平均误差略微增加。为弥补这个数学期望引起的预测平均误差,需要在预测前给出该数学期望足够准确的估计。将对数变换进行泰勒级数展开,并采用前四项进行解析分析,得出高斯白噪声经过对数变换后的数学期望和方差。这些结果明显改进了2008年Cryer和Chan使用前两项的结果。数值实验证实了该数学期望和方差计算式的准确性。采用五种模型对公路交通流预测时,可以有效解释对数变换形成的平均误差-0.5570。
Logarithmic transform not only can remove the＂long-term trend＂in nonstationary time series,but can also obviously reduce the fluctuation ranges of ＂seasonal＂and ＂residual＂stochastic fluctuation,thereby reduces the mean squared error of forecasting. However a small nonzero mathematical expectation may form after applying logarithmic transform on white Gaussian noise,this causes a slight increase in mean error of forecasting. In order to make up this forecasting mean error incurred from mathematical expectation,the mathematical expectation should be accurately estimated well enough before forecasting. By applying the Taylor series expansion on logarithmic transform and analytically explaining it with preceding four terms,the mathematical expectation and variance of white Gaussian noise after the logarithmic transform executed are derived. These results obviously improve the results of Cryer and Chan using preceding two terms in 2008.Numerical experiments confirm the accuracy of mathematical expectation and variance calculation formulas. When applying five models to forecast the highway traffic flows,it is able to explain the mean error- 0. 5570 formed by logarithmic transform.
出处
《计算机应用与软件》
CSCD
2015年第12期38-41,共4页
Computer Applications and Software
基金
天津市科委科技计划项目(13ZXCXGX40400)
关键词
非平稳时间序列
预测
对数变换
数学期望
平均误差
交通流
Nonstationary time series
Forecasting
Logarithmic transform
Mathematical expectation
Mean error
Traffic flows
