Phase Distribution and Phase Correlation of Financial Time Series

Scaling, phase distribution and phase correlation of financial time series are investigated based on the Dow Jones Industry Average (DJIA) and NASDAQ 10-minute intraday data for a period from Aug. 1 1997 to Dec. 31 2003. The returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of Levy's alpha stable distribution condition. A novel approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study phase distribution and correlation. The analysis of phase distribution concludes return time series fall into a class which is different from other non-stationary time series. The correlation between returns of the two indices probed by the distribution of phase difference indicates there was a remarkable change of trading activities after the event of 911 attack, and this change persisted in later trading activities.