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Phillips-Ouliaris Test is a cointegration test, and in my understanding it should be commutative. That is, the test result for series x and y and the test result for series y and x should coincide. However, the `po.test' function in tseries package in R does return different results. Why does this happen?

po.test(cbind(XUK, XEU))

Phillips-Ouliaris Cointegration Test

data: cbind(XUK, XEU) Phillips-Ouliaris demeaned = -21.662, Truncation lag parameter = 10, p-value = 0.04118

po.test(cbind(XEU, XUK))

Phillips-Ouliaris Cointegration Test

data: cbind(XEU, XUK) Phillips-Ouliaris demeaned = -17.13, Truncation lag parameter = 10, p-value = 0.09844

For your information, the sample data set is available at: www.maths.adelaide.edu.au/andrew.metcalfe/Data/us_rates.dat

Gura
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  • In general, given that $y=f(x)$ is a function does not necessarily imply that $x=g(y)$ is also a function. – Carl Nov 03 '18 at 02:45

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