Apr

13

This is a topic that keeps appearing when people talk about probability. I don't seem to have a good intuition for it. Is the stock market with memory or without memory? Why? What would be your intuitive explanation of what memory is?

From Memorylessness:

In probability and statistics, memorylessness is a property of certain probability distributions. It usually refers to the cases when the distribution of a "waiting time" until a certain event occurs does not depend on how much time has elapsed already. To model memoryless situations accurately, we must constantly 'forget' which state the system is in: the probabilities would not be influenced by the history of the process.

Only two kinds of distributions are memoryless: geometric distributions of non-negative integers and the exponential distributions of non-negative real numbers.

Humbert H. responds:

Of course it's not completely memoryless otherwise there would be no point to any spec of this list trying to beat the market. It's ALMOST memoryless, and that's why it's hard to beat, but there are still some irregularities, like days of the week, month, season, reaction to events, like increased volatility following a big change. It would have a lot more memory if people didn't try to take advantage of the irregularities, because market participants have emotions and also information doesn't spread instantaneously even in this day and age.

Eric Lindell comments:

Blackjack is with memory, provided the number of decks is finite. As you play with more and more decks, the game becomes less memory-dependent. A small player in a huge market makes trades that are less memory-dependent than a big player's trades. The bigger the portion of the total market a trader trades, the more memory-dependent it becomes.

Wikipedia's discussion of a memoryless probability distribution refers to a poisson process. The time before the next car arrives at a toll booth doesn't depend on the time since the last car arrived — provided the cars' arrivals are truly random. This would NOT be the case with a nonrandom distribution, as when more cars arrive per minute during rush hour.

Zubin Al Genubi writes:

A normal distribution of a series of events, indicates that the events are independent of each other, in that the occurrence of one does not affect the probability of another. Of course the market has memory and emotion. We are looking for the regularities to trade that are not random with a high degree of confidence.

Larry Williams agrees:

Amen! People react in similar fashion to events and those reactions create patterns. Plus, there are unique time elements to many markets; jewelry is mostly sold at Christmas, hogs live and die in 18 months etc.

Penny Brown adds:

Investors who suffer a big, sudden decline in a stock remember it. Often they vow to hold on until they are made "whole". This can cause a stock to sell off as it approaches that spot. But if the stock clears this area, the weak hands are gone, and the stock can move up sharply.

Big Al suggests:

For further study, re the quality of "memoryless" and possible applications:

Markov chain

Hidden Markov model

Also, Vic has referred to Markov processes relating to the market calendar at the top of this site.


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