Using ADF Tests to Compare Cointegration Strength

Summary

The document asks whether cointegrated time-series pairs can be ranked by how strongly they are cointegrated. It seeks an intuitive comparison for identifying which candidate series is most closely cointegrated with a given series, down to the weakest pair.

The brief accepted answer points to the Augmented Dickey–Fuller test as a usual tool for this purpose. However, it gives no procedure for turning test results into a robust ranking, and offers no examples, diagnostics, or empirical evidence. ADF results are test statistics for a specified residual or series setup, so the document alone does not establish that they provide a universal measure of cointegration strength. The suggested approach should therefore be treated as a starting point for investigation rather than a fully explained ranking method.

Key ideas

• The question concerns ranking candidate pairs by the apparent strength of their cointegration.
• The answer identifies the Augmented Dickey–Fuller test as a commonly used tool.
• The document gives no detailed ranking procedure or worked comparison.
• It does not establish a universal intuitive measure of cointegration strength.

Tags

# Is there a measure for the 'degree' of cointegration


# Is there a measure for the 'degree' of cointegration












Is there a standard (or maybe even intuitive?) way of ranking pairs of cointegrated time series so that one could make statements like the following:

```
series A is MOST cointegrated with series M
series A is NEXT MOST cointegrated with series Y
...
series A is NEXT, ... NEXT (i.e. LEAST) cointegrated with series J
```

## Answer by strimp099 (score 4, accepted)

https://quant.stackexchange.com/a/2863

The Augmented Dickey–Fuller test is usually used for this purpose. Again, wikipedia does a decent treatment.

I would suggest using google for this before posting here. There is tons of information out there on cointegration.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.