1/f behavior in cross-correlations between absolute returns in a US market

Employing detrended fluctuation analysis (DFA) and detrended cross-correlations analysis (DCCA), we analyze auto-correlations in the absolute returns for each of 30 Dow Jones Industrial Average (DJIA) constituents, Si, and cross-correlations in the absolute returns between the DJIA and each Si. We find that each DJIA member follows the DJIA in absolute returns, since the DCCA curve for each pair (Si,DJIAi) exhibits strong cross-correlations, with average DCCA exponent 〈λ〉=1.03±0.04. This value for 〈λ〉 implies that the power-law cross-correlations are of the 1/f functional form. For the financial firms comprising the DJIA, we also find that the DFA and DCCA exponents controlling the duration of firm risk are somewhat larger than the corresponding values for the rest of the US financial industry.