  We present a relatively detailed analysis of the persistence probability
distributions in financial dynamics. Compared with the auto-correlation
function, the persistence probability distributions describe dynamic
correlations non-local in time. Universal and non-universal behaviors of the
German DAX and Shanghai Index are analyzed, and numerical simulations of some
microscopic models are also performed. Around the fixed point $z_0=0$, the
interacting herding model produces the scaling behavior of the real markets.
