Analysis of correlation matrice, copula and Epps effect in stock market for various time intervals

Abstract

Analysis of correlation matrice with Random matrix theory(RMT) is well known in daily stochastic data. We conduct making correlation matrice in various time intervals, different from the previous study. RMT is also available in most of cases using the various time intervals, but the components of $u^{largest}$ has different shapes of distributions as time intervals change. It is effective not in short time intervals but in long time intervals. Also, the shifts of pdf of coefficients support the same conjecture. The largest eigenvalues show Epps effect, but not enough to explain due to the change of $u^{largest}$ . The dependence structure of Cook-Johnson copula relies on a copula parameter, and the increase of a copula parameter makes sure the structure of correlation matrix stronger as time interval increases. They imply an anlysis for correlation matrix requires the time interval long enough with RMT, and multiasset Epps effect is also available.