Dude, just give me the cointegration percentage

“Dude, you can get cointegration measures from at least 4 different products and services on the net – and they all boil it down to a single percentage for me.”

If that’s your view, please go back and check that percentage carefully. Cointegration cannot be usefully reduced to a single number. If you are relying on that percentage and calling it cointegration what you likely have is the result of a statistical test called the Augmented Dickey Fuller (ADF) test. Don’t take our word for it: ask the provider of the stat what’s behind it.

An ADF test is not by itself a test for cointegration. Happily, at least one of those services does at least describe the ADF method they are using as a probability that a pair is cointegrated (which is also an arguable contention).

This is a very, very important distinction. Cointegration tests require analysis of residuals (see our glossary for the definition if needs be). For example, ADF testing the pair JOYG/DV returns an alleged cointegration of over 96% according to promoters of this method (with the number coming direct from one of their services). Sounds fantastic!

Unfortunately, JOYG and DV are not, in fact, anywhere near cointegrated – which a test of the residuals using the Engle Granger method would show. And that’s the case over the last year, 2 years, 3 years, 4 years, 5 years, 6 years, 7 years, 8 years, 9 years and 10 years. Earlier data is not available.

There are many ways to skin a cat. A service that talks about cointegration based on a single figure might still be making a great overall tool for its users. But it won’t be one that uses the cointegration analysis invented by Nobel Laureates Mr Engle and Mr Granger.