| We see that most real data do not share the properties of Brownian motion. |
| The comparisons
are clearest when we view differences instead of the raw data. |
| Here are difference graphs for two
examples of Brownian motion. |
| For comparison, below these are difference graphs for four years
of EMC closing prices (left) and Dell closing prices (right). |
|
| For later reference we note that when the thickness of the plotting line is
approximately equal to the spacing between successive values, the bulk of the difference plot
merges into a band. |
| Further, for Brownian motion (top two graphs) we observe |
| 1. The band is of approximately constant width. |
| 2. The outliers are relatively small (this is called the
short tails property). |
| 3. The outliers are approximately uniformly distributed. |
| How well do real data satisfy these conditions? At least for EMC and Dell,
the match appears to be weak. |
