论带有趋势变化的变量的相关:数值试验  

On the Correlation of Variables Containing Secular Trend Variation: Numerical Experiment

作　　者：施能[1] 顾骏强[2] 封国林[3] 

机构地区：[1]南京信息工程大学气象灾害和环境变化重点实验室,江苏南京210044 [2]浙江省气象科学研究所,浙江杭州310017 [3]国家气候中心气候研究开放实验室,北京100081

出　　处：《数学的实践与认识》2007年第8期98-103,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(40275028)

摘　　要：当计算相关的二个变量都包含有明显的趋势变化成分时,原变量之间的相关特征可能被歪曲(夸大或者缩小).对此问题进行了数值试验,结果表明,变量带有性质相反的趋势变化,会使这二个变量之间的相关系数减小(正相关的数值减小,负相关被夸大).变量带有性质相同的趋势变化,会使这二个变量之间的相关系数增加(正相关被夸大,负相关数值变小).数值试验还表明,趋势变化对相关的影响具有可交换性.只要不改变它们趋势变化的数值,它们叠加的变量互相交换,影响相关系数的后果是一样的;研究还指出,二个变量有相同的变化趋势时,对相关的影响会更大些.给出了实例.This paper points out that when calculating the correlation of two variables containing obvious secular variation component,the interannual variation characters between the two variables may be distorted(overestimated or underestimated).Numerical experiments in this paper show that if two variables have opposite secular trends,the correlation coefficient between the two variables is reduced(the positive correlation is underestimated,or the negative correlation is overestimated);and if two variables have same sigh secular trends,the correlation coefficient between the two variables is increased(the positive correlation is overestimated, or the negative correlation is underestimated).Numerical experiments also suggest that the effect of secular trend variations on the interannual correlation of two variables is interchangeable,as long as the values of their trend variations are not changed,two variables on which the two trends are superposed respectively are interchanged,the effect on the correlation is the same;if the two variables contain the same trend,the effect of secular trends on the correlation are more distinct.A meteorological example is also given.

关 键 词：相关分析 长期趋势 趋势系数 数值试验 

分 类 号：O211.9[理学—概率论与数理统计]