| Here are
two graphs, one the closing price of IBM stock from 1959 to 1996, the other
is Brownian motion. Can you tell which is which? |
|
| Here are the corresponding successive differences:
left
and
right.
Now can you tell which is which? |
| The first difference plot reveals both
long tails and
dependence, while the
second shows neither tendency. |
| The second is
Brownian motion, the first is real
data. |
| The difference plot shows these features clearly, while the plot of closing
prices is not so easy to interpret. |
| This is one of the strengths of plotting
differences. |
