# Sampling Without Replacement, from Victor Niederhoffer

January 11, 2009 |

Sometimes one sees almost every conceivable variations of prices during the year. It's like an evil genius had a bag of tricks and never had to repeat one exactly the same way. I wonder if it's possible to turn this around and assume that there is a finite number of tricks, possible variations that will occur and then predict that the ones not used yet will eventually be used. This becomes particularly relevant for people who look for repetitions of past patterns and in days like this find that there is nothing similar to it in history. Regrettably, that is true almost every day. There should be some creative ways of testing this.

We could look at market entropy, in an information theoretical sense:

Code every possible pattern in bit form, eg 1110011000111

Measure entropy.

See if the market is maximizing it, this would be the "Second Principle of Market Dynamics".

We could also have a Prigogine's Theorem analog i.e the market is forming patterns that will minimize its entropy production.

As an analogous situation, I believe that slot machines, keno games, etc. have their results or numbers selected by random number generator formulas. I always thought that if one is an expert on the existing formulas or was able to generate a random number generator formula based on a series of outcomes then he could beat the game.

I realize that the casino could easily thwart this in keno but it would take additional work on their part for the slots.

In the stock & futures market, I understand there is some pattern recognition software now available. I have no experience with it.

## James Sogi writes:

Maybe sampling something simple like variance over the last couple days might give one a clue. Volatility clusters, and lack of volatility clusters, and variance of volatility within those clusters or length of the clusters, or the survival rates. Again the replacement issue and the assumption of independence clash. The replacement assumes independence, but a cluster model assumes some correlation.

A related (and very important) topic is the number of stable patterns achievable by a set of interconnected nodes. On this topic, a worthwhile read is Stuart Kauffman. Kauffman's work is rather well presented in a chapter of Deep Simplicity: Bringing Order to Chaos and Complexity , John Gribbin, Random House. 2005. ISBN 1-4000-6256-X.

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