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A network topology approach to diagnose the shift of covariance structure

Understanding the shift of covariance matrices in any process is not an easy task. From the literatures, the most popular and widely used test for covariance shift is Jennrich’s test and Box’s M test. It is important to note that Box and also Jennrich have constructed their own test by involving sample covariance matrix determinant or, equivalently, generalized variance (GV) as multivariate variability measure. However, GV has serious limitations as a multivariate variability measure. Those limitations of GV motivate us to use a proposed test based on an alternative measure of multivariate variability called vector variance (VV). However, if after hypothesis testing the hypothesis of stable process covariance is rejected, then the next problem is to find the cause of that situation. In this paper, network topology approach will be used to understand the shift. A case study will be discussed and presented to illustrate the advantage of this approach