多尺度突变现象的扫描式t检验方法及其相干性分析

阐明了将检测两子样本平均值之差的学生氏t检验推广到对多尺度突变现象进行扫描式检测的计算方法；对于t检验要求序列独立的限制，引用了初步的订正方法；还给出了检测两个序列间多尺度突变相干性的计算公式.扫描式t检验不仅具有相当于子波变换检测多尺度突变现象的功能，而且解决了子波变换检测突变时缺少临界值的问题.由于t统计量包含有二阶矩均方差，它不能像子波变换那样作为分解工具，但检测的尺度参数也就不必局限于2的整数幂，因而可以进行扫描式检测.应用于尼罗河年最高与最低水位历史序列(AD622-1470)，能较客观和精确地检测出两序列在某些尺度上的相干性(同步或反位相)变化；并由此重新划分了该流域几十年至百余年时间尺度的相对干湿期.结果与目前查阅到的埃及灾荒历史记载相吻合.

A SCANNING t TEST OF MULTISCALE ABRUPT CHANGES AND ITS COHERENCE ANALYSIS

A scanning t test of multi-scale abrupt changes is introduced byextending the student t test,which detects the difference between two subsample means. It is shown that this algorithm has not only the capacity similar to Haar wavelet transform coefficient W(a,b) for detection of multi-scale abrupt changes,but also gives the statistic significance threshold,which the wavelet analysis can not do. The subsample size n (comparative to the scale parameter a in W(a,b)) of the statistic t(n,j) may vary successively without limitation of integer power of 2 as in the wavelet transform for a discrete series,so that the algorithm may detect any longer signal series like a scanner. However,this algorithm is not a decomposition tool because the second momentum,the variance,is involved. In addition,a correction to the Effective Degrees of Freedom (Ef) of t test is adopted for the dependency of an observation series to be detected. A coherence detection of abrupt changes between two signal series is carried out. The results of an application to historic series (AD622-1470) of the maximum and minimum flood levels of the Nile River reveal objectively that there appears some abrupt changes in phase and out of phase on certain scales between the two series. The relative dry and wet phases on around 0.5—1.5 century scale are further repartitioned following this detection. And these dry/wet phases coincide better with historic records of catastrophe in Egypt found so far and are some improvements upon previous researches.