As an example, we collect time series of daily closing prices of six stocks, 
AIVSX (Investment company of America), APPL (Apple), CSCO (Cisco), GE, IBM, and INTC (Intel) 
All data go to June 8, 2005, and have these starting dates 
AIVSX  June 3, 1996  2270 trading days 
CSCO  March 26, 1990  3834 trading days 
INTC  July 9, 1986  4774 trading days 
APPL  Sept 6, 1984  5237 trading days 
IBM  Jan 2, 1962  10934 trading days 
GE  Jan 2, 1962  10934 trading days 

The f(α) curves were generated by the method of moments using
our fractal statistics software, with
q ranging from 20 to 20, an α step of 0.01, and a
q step of 0.1. 
To illustrate this, use the
Intel data. 
Here are other data sets we use.
APPL,
AIVSX,
IBM,
GE, and
CSCO. 
In all windows, the horizontal axis (α) ranges from 0 to 2 and the vertical axis (f(α)) ranges
from 0 to 1. 
For comparison, here are the
time series and the
driven IFS. For
the driven IFS we plot differences using meancentered bins with first and third bin boundaries one standard deviation above and below the
mean. 

Finally, here are the observed α ranges. 
AIVSX  .90 <= α <= 1.73  APPL  .87 <= α <= 1.11 
CSCO  .68 <= α <= 1.29  GE  .87 <= α <= 1.78 
IBM  .78 <= α <= 1.47  INTC  .77 <= α <= 1.50 
