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. The standard practice of stock network analysis is still too far from reality. It involves Pearson correlation (PC) to quantify the similarity among stocks based on closing price only, and the minimum spanning tree (MST) to filter the economic information. In daily practice, stock is represented by its four prices: the opening, highest, lowest, and closing prices. To incorporate the information from these prices, vector correlation is used instead of PC. Furthermore, to get robust network topological properties, the MST is replaced by the forest of all possible MSTs. Its advantages is demonstrated in the analysis of 1515 stocks traded in the New York Stock Exchange from 2005–2014.

A lot of studies dealing with stock network analysis, where each individual stock is represented by a univariate time series of its closing price, have been published. In these studies, the similarity of two different stocks is quantified using a Pearson correlation coefficient on the logarithmic price returns. In this paper, we generalize the notion of similarity between univariate time series into multivariate time series which might be of different dimensions. This allows us to deal with economic sector network analysis, where the similarity between economic sectors is defined using Escoufier’s vector correlation RV. To the best of our knowledge, there is no study dealing with this notion of economic sector similarity. Two examples of data from the New York stock exchange will be presented and discussed, and some important results will be highlighted.

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.