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I am studying cointegration theory in time series using online resources.

As per https://www.econometrics-with-r.org/16-2-ooiatdfglsurt.html

DF-GLS test is implemented in the package urca can be used to test for cointegration, but the null hypothesis of this test is to check for unit root in zt=xt- \theta*yt.

There are other R functions that provide the cointegrating vector (e.g., VECM function in tsDyn package, ca.jo function in urca package), but I could not find a way to do any hypothesis testing on the estimated cointegrating vector.

To be specific, how do I test if this cointegrating vector (1, \theta) is equivalent to (1, -1) ?

I found a related question here, but not specifically on hypothesis testing.

Test for cointegration between two time series using Engle–Granger two-step method

Please advise.

Meenakshi S
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    hi: when you do engle granger, ultimately ( at the last step ), you run a regression. a test of beta = -1 in that regression is the test of the cointegrating vector being (1, -1). – mlofton Jul 23 '20 at 14:20

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