A new statistic to the theory of correlation stability testing in financial market

Abstract

Testing the stability of correlation structures is an active research area involving the applications of multivariate analysis in financial market such as stock market analysis, risk management, market equity, general financial and economic studies, and real estates. In the financial market, the number of variable p is usually large and might reach thousands. As a consequence, the standard stability test Box’s M and Jennrich’s statistic are not capable to handle it. This condition makes the computation of the statistical tests quite cumbersome and tedious because the computational efficiency of finding the determinant and inverse of the correlation matrix becomes low. In order to solve these problems, this thesis introduces T*-statistic for testing the stability of correlation structure in an independent sequence of sample correlation matrices from a p-variate normal distribution based on a repeated test approach. For this purpose, the asymptotic distribution of the test under the null hypothesis is derived mathematically using the vec operator and commutation matrix. The power of T*-statistic is computed and compared with existing ones under certain conditions of the alternative hypothesis. It is found that, if p is large, then the power of T*-statistic dominates the power of the J-statistic for all shifts. On the other hand, when the shift is small, its power is equal to that the Mstatistic. The second problem is to diagnose and find an explanation when the null hypothesis is rejected. For that purpose, by considering correlation matrix as representing a complex network, network topology approach is used to demonstrate to what extent that two or more correlation structures are different from each other. To interpret the filtered network topology, four popular centrality measures have been used. Moreover, to enrich the economic interpretation, average of weights is introduced as another measure of centrality.