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. |