It is not a bug but it’s easy to assume so.
We are running the Engle-Granger methodology which uses the Augmented Dickey Fuller (ADF) test. For the ADF the null hypothesis states that ‘this data series is non-stationary’ or, in other words, that the series has a unit root.
For cointegration to be valid time series data must meet two pre-requisites
- The original prices of the series must be non-stationary. Thus if the null hypothesis above cannot be rejected the next test is
- Are the differences of the ordinary prices stationary? This requires rejection of the null.
When conditions (1) and (2) are met the residuals can then be tested for stationarity – if they are in turn stationary then the two series are cointegrated. Each test leaves us with a t-stat which we then compare to ADF critical values to determine rejection or non-rejection of the null. The critical value at 5% is -2.86; and 1% is -3.43.
An example. We test condition (1) at 5% and generate a t-stat of -2.98. The null hypothesis demands verification the series is not stationary. That is, if the t-stat is less than the 5% critical value you can reject it – which it is in this example. And so the red fail colour is applied in the software.
But -2.98 is more than the 1% critical value. So at that level we cannot reject the null – which produces a green pass. Counter-intuitive but correct.
Conversely, when testing condition (2) what we are looking for are t-stats that are less than the critical values. Thus a t-value that satisfies at 1% necessarily does so at 5%.
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