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Hello,

I have doubts about interpretation of the Single-Equation Cointegretion Test results. Engle-Granger test gives two types of statistics - tau-statistic and z-statistic. According to p-values there is a discrepancy in both statistics (95% confidence level). Which one gives result of the tested hypothesis that there is no cointegration?

Series: Series A Series B
Sample (adjusted): 1993 2014
Included observations: 22 after adjustments
Null hypothesis: Series are not cointegrated
Cointegrating equation deterministics: C @TREND @TREND^2
Automatic lags specification based on Schwarz criterion (maxlag=4)



Dependent tau-statistic Prob.* z-statistic Prob.*
Series A -3.647562 0.2903 -27.79631 0.0027
Series B -4.096864 0.1620 -40.57648 0.0000


*MacKinnon (1996) p-values.

Intermediate Results:
Series A Series B
Rho - 1 -0.666481 -1.136997
Rho S.E. 0.182720 0.277529
Residual variance 1.05E+09 0.018064
Long-run residual variance 4.56E+09 0.057516
Number of lags 1 1
Number of observations 20 20
Number of stochastic trends** 2 2


**Number of stochastic trends in asymptotic distribution



Thank you for any help

While there is always the possibility of discrepancy between the single-equation cointegration tests run with different dependent variables, from the posted output, the tests are in agreement up to size alpha ~ .003, which corresponds to about a 99.7 confidence level.