On distributional behavior of Jennrich's statistic

For testing the hypothesis that correlation structure is stable from sample to sample,jennrich's statistic is the most appropriate tool. however,when the dynamics of that structure is of our interest,it becomes useless. this is due to a serious limitation it possesses; as a finite sum of independent statistics,the distribution of each term is unknown even asymptotically. on the other hand,understanding such dynamics is very important. it will enable us to monitor where and when the correlation structure has significantly been shifted. to overcome this problem,we introduce a correction factor for each term of that statistic and then derive the asymptotic distributional behavior of the corrected statistic.