Monday, December 12, 2005

Get Fooled By Randomness!

by Tom Bozzo

Via Marginal Revolution, here's a web survey run by a couple of University of Basel grad students that tests the ability to discern graphs of actual stock prices from artificially-generated "random walk" processes (i.e., the price changes are random). Like Alex Tabarrok, I did well, but then again I wrote my dissertation in part on the behavior of a type of random walk, so it would be embarrassing if I didn't do well. Try it out!

(Warning, spoilers ahead!)

I would put my secret in invis-o-text, but I think enough regulars use aggregators that throw away formatting information that I won't bother. The secret, put somewhat loosely, is that you should look for an absence of mean reversion. Depending on the exact generating process of the steps to a random walk, they can move quite rapidly in one direction or another, and stay there (since that's the conditional mean of the subsequent path). But it's very unlikely that a true random walk will move predominantly in one direction for a long time — that would be like flipping a coin lots of times and getting all heads; that's not impossible, but it's sufficiently unlikely that after a while you might consider nonrandom causes.
Thanks for your participation!

Unfortunately, you could not identify the Random Walk. However, both your predictions were correct.
Interesting. I didn't even try to play technical analyst with the real stock prices. For the random walk, the distribution of the endpoint is centered in wedge C, but the correct answer would be a roll of the virtual dice.
How do you do invis-o-text. Do you mean, just make it the same color as the background so people can see it if they highlight?
That's what I mean here... I'm swiping the usage from Ain't It Cool News. The same issue would seem to apply to Blogger implementations of expandable posts -- my RSS aggregator ignores the 'jumps.'
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