Is this a proper way to think of cointegration? If two stocks, bonds, whatever are cointegrated, then their prices cannot diverge away from each other for too long without returning to some mean distance between the two. If that is the case then when you test for this what says you have two cointegrated variables and what says you dont?
I would change your analogy from too long to too far. It intuitively means there exists some linear combination of the pair, such that the net position will be a stationary and mean reverting process. Using this model, you could imagine shorting one and buying some multiple of the other as they diverge significantly away from each other, expecting them to converge again some time later. Look into cointigrating regression Dickey Fuller test for a start; there are several alternative statistical tests to verify the relationship. Like any model, however, there is no guarantee that the relationship will continue to exist into the future, nor if or when they will converge.
Thanks for the response. Why would you want to "buy some multiple of the other"? Could you elaborate?
My apologies to the OP for this interruption and "Red Herring" ... I am looking for something to read along the lines of "Dickey Fuller test for Dummies". Any recommendations? I have perhaps "first-year university equivalent level" knowledge of statistics. My attempts to get from there to understanding the background and rationale for the DF test have so far proved fruitless ... Any suggestions? Something readable and clear ... Thanks.
The idea is simple. You have a regression function that describes the time series at a given time as a function of its lagged values. If there is a unit root, then the relationship is not stationary and the coefficient is one. But you can't test this directly, because the usual beta = 0 test conditions don't apply -- there's no "normally" distributed coefficient divided by a chi-square variable, like there is in a t-test.
Thanks, garchbrooks Let me dust off my copy of "Understanding Statistics" once again (which does not cover DF test), to see how far I can get using your explanation ... Many thanks.
You need to understand the following statement in dtrader's response. In particular what "linear combination" means. "there exists some linear combination of the pair, such that the net position will be a stationary and mean reverting process" In addition, check this out: http://www.gummy-stuff.org/cointegration.htm
Also http://quanttrader.info/public/testForCoint.html is a step-by-step using R. BTW, much money has been lost over the years by traders who <i>thought</i> a pair of securities was cointegrated.