非定长相关时间序列集内平均序列的摆动异常及其解释  

ON THE ABNORMAL SWING OF THE AVERAGED TIME SERIES PRODUCED FROM A NUMBER OF CORRELATED TIME SERIES

作　　者：刘洪滨[1] 周江兴[1] 

机构地区：[1]国家气候中心,北京100081

出　　处：《气象学报》2003年第4期488-493,共6页Acta Meteorologica Sinica

基　　金：国家"十五"科技攻关项目(2001BA611B-01);中国科学院知识创新工程重要方向项目(KZCX3-SW-321)

摘　　要：文中对多个时间序列的平均序列中常常出现的异常摆动问题进行了探讨。结果表明,给定时间序列集中序列个数的多少会造成其所组成的平均序列的方差的变化,即序列个数越多,平均序列方差越小的可能性就越大,由此定义了方差增长率α。当给定方差增长率限定值α_0并使其满足α≤α_0时,可以得到最小序列个数m_0,且α_0越大或序列间平均相关系数越大,所需要的时间序列数越少。这一结果可应用于气候变化研究中有关平均时间序列建立的研究中,亦可运用到其他相关研究领域。In many climatological researches, the averaged time series can be produced from a number of time series to enhance common signals. The abnormal swing always exists in the averaged series, so that the changes of the former part of the series, with less samples, are larger than those of the latter part, with more samples. This phenomenon could be found either in tree ring chronologies produced from tree ring series with different lengths or in the averaged time series of some climatic parameters produced from records of meteorological station network. We suppose that there is a series set defined as X including m time series (m > 1). So in X, there are Cmm' (m≥m'≥1) series subsets km'X(k∈ [1, Cmm']), including m' time series. For each subset km'X,km' S is the variance of the averaged series of all time series in the subset .m' S is the mean value of all variances km'S with m' time series. So,m' S could be taken as the variance of the averaged time series of m' time series with maximum possibility. Term r is the mean value of each inter - series correlation coefficientin set X. The m'S value would be getting smaller as the series number m' getting larger, namely,mn S≥m' S (m≥ m'≥m''≥1). Then, variance increasing rate a and minimum series number m'0 are define as where a0 is the limit value of a . That is to say, when the value a0 is given to make a satisfy a≤a0 , the series number m' should satisfy m'≥m'0. When m→+∞ , term m'0 would be expressed as These results are applied to determine the uncertainty in any conditions when averaged time series is produced from a number of time series with .different lengths. The terms defined here are useful for the researchers to make decision how long an averaged series (like tree ring chronologies) could be used with lower uncertainty.

关 键 词：时间序列 方差均值 气候变化 平均序列 异常摆动 

分 类 号：P467[天文地球—大气科学及气象学]