Quote:
Originally Posted by gangip
rand,
Is your claim that a random walk with drift is more predictable than one without drift because you kinda know which direction it's heading?
Wouldn't a random walk without drift be equally predictable? You still have a good idea of where it should end up, it just so happens to be not much of a change.
In short yes to the first part, and no to the second.
One of the best and simplest ways to model a random walk is with the flipping of a normal coin (ignore edge cases obviously).
The second (random walk w/out drift) would only be true if there were some kind of relationship between flips. Like if getting 100 heads makes tails more likely on the next flip. This is a common mistake at the roulette wheel and why casino's display histories there.
You wouldn't know in the later case
because (with a legitimately random walk) each trial is independent.
It is, interestingly enough, another point against random walks in the markets. Almost everyone with a clue talks about overbought and oversold. The idea of reversion to the mean. If markets revert to the mean (hint: they do) then the trials are not independent.
Coin flip trials do not revert to the mean. Their expected value is the mean, but if you actually flip a coin 100 times, the odds that you will get 50 heads and 50 tails is pretty low. If you do that 101st flip however, the odds that you will get heads or tails on that trial is still 50/50.