Granger's Solution to the Drunkard's Walk

The Full Article is at the source *

Granger's principal contribution, for which he would ultimately share the Nobel Prize in Economic Sciences in 2003, was in developing methods to analyse the behaviour and links between economic time series.

In the 1970s Granger and Newbold published an article in which they demonstrated how apparently significant statistical relationships between economic time series were in fact misleading (Journal of Econometrics, 1974). They found that spurious relationships of this sort were driven by integrated economic variables that tend to wander over time without returning to some long-run resting point, an effect first noted by GU Yule in the Journal of the Royal Statistical Society in 1926.

A simple analogy can again be drawn using the drunkard's walk. Suppose our drunkard is accompanied by his two faithful dogs. If we looked at the behaviour of the dogs in isolation they, like the drunk, would appear to follow random walks, yet the difference between their positions and the drunk are both, on average, constant. Here the drunk is the common trend.

The discovery of co-integrated relationships allows several of these "wandering" integrated variables to be combined in a way that allows for the reliable application of standard econometric methods, and it was this contribution that led Granger and Engle to be awarded the Bank of Sweden Nobel Memorial Prize in Economic Sciences in 2003.

* For the full article read the source which is given full credit for the above copy and shown at the url below:
http://www.guardian.co.uk/education/2009/jun/01/obituary-sir-clive-granger?INTCMP=SRCH
Note: You might have to do a search as the source above changes from time to time.

Example of Cointegration as a Solution to the Drunkard's Walk **

Definition: If there exists a stationary linear combination of nonstationary random variables, the variables combined are said to be cointegrated.

The old woman and the boy are unrelated to one another, except that they are both on a random walk in the park. Information about the boy's location tells us nothing about the old woman's location.

The old man and the dog are joined by one of those leashes that has the cord rolled up inside the handle on a spring. Individually, the dog and the man are each on a random walk. They cannot wander too far from one another because of the leash. We say that the random processes describing their paths are cointegrated.

** Above cointegration example, comments and animations are credited to Andrew J. Buck of Temple University.