基于傅立叶变换的统计数据外推问题研究  

Research on Statistical Data Extrapolation Based on Fourier Transformation

作　　者：郭建平 曹杰 仲坤[2] 赵立龙[2] Guo Jianping;Cao Jie;Zhong Kun;Zhao Lilong(School of Management Science and Engineering,Nanjing University of Inormation Science&Technology,Nanjing 210044,China;School of Physics&Optoelectronic Engineer,Nanjing University of Inormation Science&Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学管理工程学院,南京210044 [2]南京信息工程大学物理与光电学院,南京210044

出　　处：《统计与决策》2020年第13期30-33,共4页Statistics & Decision

基　　金：国家社会科学基金重大项目(16ZDA054);教育部人文社会科学研究规划基金项目(19YJA630023)。

摘　　要：文章提出了一种基于傅立叶变换的数据外推方法,通过将数据分解为有限谐波分量的线性组合实现数据外推。首先,依据傅立叶变换,确定较大振幅对应的频率和相位;然后,根据频率、振幅和相位确定谐波分量的三角函数形式,把原始观测数据分解为有限个三角函数的线性组合;最后,依据解析式,计算相应函数值,获得外推数据。使用移动平均方法对原始数据进行外推,通过均方误差比较外推精度,数值计算结果表明,基于傅立叶变换的外推结果显著优于移动平均方法外推结果。This paper proposes a data extrapolation method based on Fourier transformation,which realizes data extrapolation by decomposing the data into linear combination of finite harmonic components. Firstly, the frequency and phase corresponding to the relatively larger amplitude are determined according to Fourier transformation. Then, according to frequency, amplitude and phase,the trigonometric function form of harmonic components Extrop extrapolate is determined to decompose the original observation data into linear combination of finite trigonometric function. Finally, according to the analytical formula, the corresponding function values are calculated to obtain the extrapolated data. Numerical calculation is made by using the moving average method to extrapolate the original data and comparing the extrapolation accuracy through mean square error. The results show that the extrapolation based on Fourier transformation is significantly better than that of moving average method.

关 键 词：数据外推 傅立叶变换 移动平均 均方误差 

分 类 号：O174.2[理学—数学]