  The entropy density is an intuitive and powerful concept to study the
complicated nonlinear processes derived from physical systems. We develop the
minimum entropy density method (MEDM) to detect the structure scale of a given
time series, which is defined as the scale in which the uncertainty is
minimized, hence the pattern is revealed most. The MEDM is applied to the
financial time series of Standard and Poor's 500 index from February 1983 to
April 2006. Then the temporal behavior of structure scale is obtained and
analyzed in relation to the information delivery time and efficient market
hypothesis.
