Correlation and Co-integration

As mentioned in an earlier posting, correlation models do not necessarily capture the directionality between variables.  We showed an example where asset prices whose changes are positively correlated may still trend in opposite directions.

Co-integrated time series, are becoming more and more important in financial econometrics, and attempt to capturing the directionality between variables.  This is something that requires a different modelling approach, such as establishing the long-run equilibrium of the spread, ratio, or differences between the prices and then modelling these. 

An example of co-integrated series is shown in the screenshot.  This statistical analysis was completed with Monte Carlo software @RISK for Microsoft Excel. In the series, a relationship has been established between the price levels of two assets, with random and uncorrelated changes to each of the levels.  From each sample of the series, the price changes can be calculated and the correlation coefficient between the series worked out. There is a positive (but varying) correlation coefficient as a result of the link between the price levels.  The average correlation coefficient in this example (calculated by conducting 1000 iterations, to generate 1000 samples of the correlation coefficient is about 44%.

Dr. Michael Rees

Director of Training and Consulting

One comment

  1. This is a valuable note, thanks. However I do not think Co-integration or VAR analysis tells all abt the causality. Before begining analysis still you need to make some subjective judgements on the flow of information, which helps you in ordering of the variables. That is, I mean to say about Wold Causality. I do not know any automated way to study wold causality, only economic/fundamental/subjective understanding may give some choice on that.

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