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ince the periodic extension of mean generating function in regression analysis has the defect of unequal premise, and the predictors are not independent to the predictants. An improving scheme is suggested. Analysis and experiments of samples result in that the new scheme can effectively eliminate the false correlation appearance which exist in old scheme, so the selected periodic predictors are more objective. Basing this new mathematical model, fitting rate and forecast accuracy is basically identical....

ince the periodic extension of mean generating function in regression analysis has the defect of unequal premise, and the predictors are not independent to the predictants. An improving scheme is suggested. Analysis and experiments of samples result in that the new scheme can effectively eliminate the false correlation appearance which exist in old scheme, so the selected periodic predictors are more objective. Basing this new mathematical model, fitting rate and forecast accuracy is basically identical. It is a very useful method for longterm prediction and analysis. What is more, this model has some resolving power of hidden periodicity.

针对均值生成函数的周期性延拓在回归分析中存在的回归前提不同,预报因子是预报量的非独立表现等缺点,给出了改进方案。实例分析计算表明:新方案可以有效地消除原方案中存在的非独立虚假相关现象,从而使得筛选出周期性预报因子更加客观。基于本方案所建立的数学预报模型,具有历史拟合率与多步长预报精度基本一致的特点,是一种具有使用价值的长期预报手段,也有一定的隐含周期分辨能力。

For the purpose of obtaining a higher correlation coefficient in form,people always transform two variables into sum,difference,product and quotient,in resulting“false correlation”of two stochastic variable groups which possess common component.For this reason,the paper processes from fundamental mathematic principle and homologizes moment about the origin and moment about the mean in the statistical mathematics,the author suggests the correlation coefficient and correlation moment coefficient and derivates...

For the purpose of obtaining a higher correlation coefficient in form,people always transform two variables into sum,difference,product and quotient,in resulting“false correlation”of two stochastic variable groups which possess common component.For this reason,the paper processes from fundamental mathematic principle and homologizes moment about the origin and moment about the mean in the statistical mathematics,the author suggests the correlation coefficient and correlation moment coefficient and derivates formula for calculating correlation coefficient after transforming the stochastic variables of sum,difference,product and quotient,through further analyzes the correlation coefficient characteristics after transforming the variables,the author believes that the “false correlation” method does not always obtain higher correlation efficient,sometimes it will lead to just the opposite,so that,we must pay attention.

2 积〔z=xy〕  乘数与被乘数可以互换而不影响其积。因此,对于由两变量之积与其中一个变量,无论是乘数或被乘数所得到的相关系数表现形式是相同的。由“随机变量积、商的统计参数计算公式”一文中①可知,变量x、y乘积的均值、均方差计算式为:均值 z=x...

This paper retrospects the history of studying“false correlation”,derives the product of four kinds of varibles and the calculation formula of correlation coefficient of second order moment and fourth order moment in analysis of false correlation of eight kinds of variable ratios and cites instances in illustration.

回顾了“假相关”的研究历史 ,推导出了四种变量乘积和八种比值的假相关相关分析的二阶、四阶矩相关系数计算公式 ,并用数例作了计算说明。

 
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