# Autocorrelation

Comment on below: “Simply put, a series of observations is autocorrelated if the value of one obsevation depends (at least in part) on the value of one or more of the immediately preceding observations…The stock market is autocorrelated. The value of the Dow Jones index at 2:00 PM is predicted by what it was at 1:00 PM if for no other reason than the 2:00 PM value must proceed the 1:00 PM value. Indeed autocorrelation is an inevitable aspect of the periodicity, trending and gradualism that one encounters regularly [when doing the crap that psychologists do]” From the lead article in Feb. March, 2008 American Psychologist (considered an important psych journal and widely read).

Well…according to the theory of martingales, the discounted share price process in an arbitrage-free market, as a random function of time, has the property that its value at any time t is the conditional expectation of the value at a future time given all the information available at time t. Stock prices are stochastic processes that fit this definition. I don’t think that the value at 2:00 pm “is predicted” by what it was at 1:00 pm, but the information known at 1:00 pm certainly plays a role in the next period’s price.

Why spend time writing an article for a journal when you could be counting your billions on the beach? I mean if I had access to that advanced knowledge of the value of the Dow for Monday at 2:00, I would most likely be taking that much needed vacation Monday at 4:01, if for no other reason than the 4pm flight “must proceed” the 2pm capital gains.

The result of a coin toss is predicted by any previous coin toss then. I was taught that the only things needed for mathematics were a pen, paper and a bin. For philosophy, you didn’t need the bin. For psychology, you clearly just need a beard.

chrismaths Wrote: ------------------------------------------------------- > The result of a coin toss is predicted by any > previous coin toss then. > That is an excellent point. > I was taught that the only things needed for > mathematics were a pen, paper and a bin. For > philosophy, you didn’t need the bin. For > psychology, you clearly just need a beard. What are you saying about beards? I haven’t seen my chin in 25 years.

JoeyDVivre Wrote: ------------------------------------------------------- > chrismaths Wrote: > -------------------------------------------------- > ----- > > The result of a coin toss is predicted by any > > previous coin toss then. > > > That is an excellent point. I don’t think that is a fair comparison. Obviously a coin toss outcome is not impacted by the result of the previous toss, but a trade at 3:01:45 certainly does partly impact what the value of the trade at 3:01:55 is.

The idea is that stock indices are something like geometric brownian motion processes. Everyone learns about those by studying coin tosses first in the S(t) = # heads in t tosses - # tails in t tosses. Scale that appropriately and you get brownian motion. Take exponent and you get geometric brownian motion. In the greater scheme of things those are about the same.

I’ll confess I don’t know jack about Brownian Motion, but I assume it is akin to Random Walk. It is fair to say that there is lots of disagreement about whether or not stock markets follow a Random Walk.

JoeyDVivre Wrote: ------------------------------------------------------- > > I was taught that the only things needed for > > mathematics were a pen, paper and a bin. For > > philosophy, you didn’t need the bin. For > > psychology, you clearly just need a beard. > > What are you saying about beards? I haven’t seen > my chin in 25 years. I confess my pognophobia. I’m just glad we don’t have profile pictures…

Sponge_Bob_CFA Wrote: ------------------------------------------------------- > I’ll confess I don’t know jack about Brownian > Motion, but I assume it is akin to Random Walk. > It is fair to say that there is lots of > disagreement about whether or not stock markets > follow a Random Walk. Brownian motion is just the continuous analogue of random walks. There is much less controversy about whether stock markets are Markov, which means that where they are going depends only on where they are not where they have been. In any event, even if stock markets aren’t Markov, their structure is very complicated and not described by any autocorrelation.