Statistical Approach to Study the Relationship Between Stock Market Indexes by Multiple DCCA Cross-Correlation Coefficient

Abstract

In this paper, we propose to analyze multiple cross-correlation between six stock market indexes (Dow Jones Industrial Average, Nasdaq Composite, DAX Performance, FTSE 100, S&P/TSX Composite and Nikkei 225) based on the multiple detrended cross-correlation coefficient, [Formula: see text]. Due to its importance and long existence, we will have as the base index, acting as dependent variable, the Dow Jones Industrial Average, which will be compared with the other five indexes in all possible combinations. In addition to calculating the [Formula: see text] for all combinations with Dow Jones, we will also infer the relative strength of each index in relation to the whole, and this will be done here through an unprecedented map of relative strength. With this map it will be possible to verify that the Nikkei 225 index has less weight for all time-scales and also all combinations, and that there is better distribution in the Nasdaq and DAX combination. Finally, we present more possibilities for this application throughout the paper.