A scanning t test of multiscale abrupt changes and its conference analysis

A scanning t test of multi-scale abrupt changes is introduced by extending 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 c hanges,but also gives the statistic significance threshold, which the wavel et analysis can not do. The subsample size n (comparative to the scale para meter a in W(a, b)) of the statistic t(n,j) may vary successively without l imitation 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 sca nner. However, this algorithm is not a decomposition tool because the secon d momentum,the variance,is involved. In addition,a correction to the Effect ive Degrees of Freedom (Ef) of t test is adopted for the dependency of an o bservation series to be detected. A coherence detection of abrupt changes b etween two signal series is carried out. The results of an application to h istoric series (AD622 - 1470) of the maximum and minimum flood levels of th e Nile River reveal objectively that there appears some abrupt changes in p hase and out of phase on certain scales between the two series. The relativ e dry and wet phases on around 0.5-1.5 century scale are further repartitio ned following this detection. And these dry/wet phases coincide better with historic records of catastrophe in Egypt found so far and are some improve ments upon previous researches.