Domino effect for world market fluctuations

In order to emphasize cross-correlations for fluctuations in major market places, series of up and down spins are built from financial data. Patterns frequencies are measured, and statistical tests performed. Strong cross-correlations are emphasized , proving that market moves are collective behaviors. 1 Statistical physics started a few years ago to investigate financial data since they seem to exhibit complex behaviors, i.e. departures from true randomness. Various physical methods have been already reported to sort out correlations in financial data [1, 2]. Recently, Bonanno et al. [3] studied data for 29 indices from different countries. The study demonstrated the existence of cross-correlations between these market places as well as a regional (continental) organization. In order to emphasize and quantify the cross-correlations between the major financial indices around the world, we present here an analysis using a different approach. Our analysis distinguish up and down fluctuations. Figure 1 presents the closing values of three major financial indices from Jan-uary 1980 till December 1999: the Japanese Nikkei, the German DAX and the Dow Jones Industrial Average (DJIA). Due to the earth rotation, the trading hours are of course different: from 9h00 till 15h00 (local time) in Tokyo, from 8h30 till 16h00 (local time) in Frankfurt, and from 9h30 till 16h00 (local time) in New York. Thus, there is only a small overlap during trading hours for the german DAX index and the DJIA. The considered period of 20 years corresponds to about 5200 × 3 data points. Below, only the sign of the daily fluctuations will be considered whatever its amplitude. Figure 2 illustrates the different sequences of spins that one can build from the three data series: (a) from the DJIA only and (b) from the three series together. Positive and negative fluctuations are represented by up and down spins respectively. During the whole period, a fraction of positive fluctuations is counted. First, let us consider each index evolution separately such as the DJIA. This evolution corresponds to the third vertical series of spins of Figure 2. For this series, a fraction b = 0.510 of " up " spins (a bias) is measured. In our analysis, only patterns of length 3 made of " up " and " down " spins, also called triplets, are considered from 3 consecutive trading days in NewYork. Thus, there exist 2 3 = 8 2 possible different triplets. Since b > 1 2 , …