  The gain-loss asymmetry, observed in the inverse statistics of stock indices
is present for logarithmic return levels that are over $2\%$, and it is the
result of the non-Pearson type auto-correlations in the index. These
non-Pearson type correlations can be viewed also as functionally dependent
daily volatilities, extending for a finite time interval. A generalized
time-window shuffling method is used to show the existence of such
auto-correlations. Their characteristic time-scale proves to be smaller (less
than $25$ trading days) than what was previously believed. It is also found
that this characteristic time-scale has decreased with the appearance of
program trading in the stock market transactions. Connections with the leverage
effect are also established.
