Pairs trading cointegration
Suppose you see two drunks i. But suppose instead pairs trading cointegration have a drunk walking with her dog. This time there is a pairs trading cointegration. Notice that although each path individually is still an unpredictable random walk, given the location of one of the drunk or dog, we have a pretty good pairs trading cointegration of where the other is; that is, the distance between the two is fairly predictable. We describe this relationship by saying that the drunk and her dog form a cointegrating pair.
In more technical terms, if we have two non-stationary time series X and Y that become stationary when differenced these are called integrated of order one series, or I 1 series; random walks are one example such that some linear combination of X and Y is stationary aka, I 0then we say that X and Y are cointegrated.
In other words, while neither X nor Y alone hovers around a constant pairs trading cointegration, some combination of them does, so we can think of pairs trading cointegration as describing a particular kind of long-run equilibrium relationship. The definition of cointegration can be extended to multiple time series, with higher orders of integration. So why do we care about cointegration?
In quantitative finance, cointegration forms the basis of the pairs trading strategy: This suggests the following trading strategy: But why do we need the notion of cointegration at all? The reason is that standard regression analysis fails when dealing with non-stationary variables, leading to spurious regressions that suggest relationships even when there are none. For example, suppose we regress two independent random walks against each other, and test for a linear relationship.
As an illustration, here I simulated pairs of random walks of lengthand found p-values less than 0. So how do you detect cointegration? There are several different methods, but the simplest is the Engle-Granger test, which works roughly as follows:. Something else that should perhaps be mentioned is the relationship between cointegration and error-correction mechanisms: By the Granger representation theorem which is actually a bit more general than thiswe then have. Hit me up if you're interested!
I work on AI, human computation, and data. Introduction Suppose you see two drunks i. Other examples of cointegrated pairs: Size of police force and amount of criminal activity Pairs trading cointegration book and its movie adaptation: Number of patients entering or leaving a hospital An application So why do we care about cointegration?
Pairs trading cointegration regression But why do we need the notion of cointegration pairs trading cointegration all? A Cointegration Test So how do you detect cointegration? There are several different methods, but the simplest is the Engle-Granger test, which works roughly as follows: Error-correction and Granger representation Something else that should perhaps be mentioned is the relationship between cointegration and pairs trading cointegration mechanisms: Dissecting the Spread of a Quora Post.
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