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 mean-centered 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 |
|