How Independent Are Stocks in an Independent Set of a Market Graph
The problem of testing hypothesis of independence of random variables describing stock returns for a given set of stocks is considered. Two tests of independence are compared. The first test is the classical maximum likelihood test based on the determinant of a sample covariance matrix. The second test is the pairwise test used for market graph construction. This test is based on testing of pairwise independence of random variables describing stock returns by Pearson correlation test. The main result is the following: the maximum likelihood test is more powerful for a wide class of alternatives. Some examples are given.
KeywordsStock Market Correlation Matrice Multivariate Normal Distribution Sample Covariance Matrix Pairwise Test
The authors are partly supported by National Research University Higher School of Economics, Russian Federation Government Grant N. 11.G34.31.0057 and RFFI Grant 14-01-00807.
- 2.Boginsky, V., Butenko, S., Pardalos, P.M.: On structural properties of the market graph. In: Nagurney, A. (ed.) Innovations in Financial and Economic Networks, pp. 29–45. Edward Elgar Publishing, Northampton (2003)Google Scholar
- 6.Emmert-Streib, F., Dehmer, M.: Influence of the time scale on the construction of financial networks. PLoS ONE 5, 9 (2010b)Google Scholar