  The conventional formal tool to detect effects of the financial persistence
is in terms of the Hurst exponent. A typical corresponding result is that its
value comes out close to 0.5, as characteristic for geometric Brownian motion,
with at most small departures from this value in either direction depending on
the market and on the time scales involved. We study the high frequency price
changes on the American and on the German stock markets. For both corresponding
indices, the Dow Jones and the DAX respectively, the Hurst exponent analysis
results in values close to 0.5. However, by decomposing the market dynamics
into pairs of steps such that an elementary move up (down) is followed by
another move up (down) and explicitly counting the resulting conditional
probabilities we find values typically close to 60%. This effect of persistence
is particularly visible on the short time scales ranging from 1 up to 3
minutes, decreasing gradually to 50% and even significantly below this value on
the larger time scales. We also detect some asymmetry in persistence related to
the moves up and down, respectively. This indicates a subtle nature of the
financial persistence whose characteristics escape detection within the
conventional Hurst exponent formalism.
