Abstract
In this paper a correction factor for Jennrich’s statistic is introduced in order to be able not only to test the stability of correlation structure, but also to identify the time windows where the instability occurs. If Jennrich’s statistic is only to test the stability of correlation structure along predetermined non-overlapping time windows, the corrected statistic provides us with the history of correlation structure dynamics from time window to time window. A graphical representation will be provided to visualize that history. This information is necessary to make further analysis about, for example, the change of topological properties of minimal spanning tree. An example using NYSE data will illustrate its advantages.
Highlights
Correlation structure among stocks in a given portfolio is a complex structure represented numerically in the form of a symmetric matrix where all diagonal elements are equal to 1 and the off-diagonals are the correlations of two different stocks
Under the assumption that pi (t ) is governed by geometric Brownian motion (GBM) law, the interrelations or, equivalently, similarities among stocks are summarized in the form of a correlation matrix C of size (n n) where its general element of the i-th row and j-th column is defined as Pearson correlation coefficient (PCC), see [1,2,14]: c(i, j ) =
The correlation structure changes will be studied by comparing the pattern of the minimal spanning tree (MST)-based network topology issued from each time window and that issued from Cpooled
Summary
Correlation structure among stocks in a given portfolio is a complex structure represented numerically in the form of a symmetric matrix where all diagonal elements are equal to 1 and the off-diagonals are the correlations of two different stocks. Larntz and Perlman [16] have remarked that the statistical model that has been advanced to test the stability of correlation structure is the one developed by Jennrich [17]. They further reported that this test has commendable properties in terms of computational and distributional behavior. As we will show, if the result is negative, Jennrich’s test cannot provide any information about the correlation structure dynamics from a time window to another. In the fourth section, a correction factor for each term in Jennrich’s statistic is introduced in order to identify the time windows where the dynamics of correlation structure. To close this presentation, concluding remarks are highlighted in the last section
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