Statistical distribution and time correlation of stock returns runs

In this paper, we focus on the statistical features and time correlation of runs which is defined as a sequence of consecutive gain/loss (rise/fall) stock returns. By studying daily data of the Dow Jones industrial average (DJIA), we get the following points: firstly, the distribution of length and magnitude of stock returns runs both follow an exponential law; secondly, runs length do lack significant time correlation, while runs magnitude exhibit a slow decay of time correlation with long persistence up to several months, which implies existence of volatility clustering. We expect the above properties may add new members to the family of stylized facts about stock returns.