Interpretation Dickey-Fuller Test

Question

ur.df(data, type = "trend", lags = 20, selectlags = "AIC")  

This is my output :

Value of test-statistic is: -3.1535 3.6559 5.1012 Critical values for test statistics: 1pct 5pct 10pct tau3 -3.96 -3.41 -3.12 phi2 6.09 4.68 4.03 phi3 8.27 6.25 5.34

From what i read i would say that at 5pct : tau3 is accepted (there is a unity root) ; phi3 is rejected since the test-statistic 5.1012 < 6.25 critique value and phi2 is rejected

where

• tau3 refers to the null hypothesis that there is a unit root.

• phi3 refers to the null hypothesis that there is a unit root AND no-trend (without trend)

• phi2 refers to the null hypothesis that there is a unit root without trend and without drift

am i missing something ? i already read

Interpreting R's ur.df (Dickey-Fuller unit root test) results

this post but i'm still not sure if i am right

Answer 1

The correct interpretation of the above example is :

we accept tau3 (null hypothesis : there's a unit root) at 5pct because -3.1535 is NOT < -3.41

we accept phi3 (null hypothesis : there's a unit root AND no-trend) because 5.1012 is not > 6.25

we accept phi2 (null hypothesis : there is a unit root without trend and without drift) because 3.6559 is not > 4.68

Answer 2

This would also be true for a 1 pct level, right?

we accept tau3 (null hypothesis : there's a unit root) because -3.1535 is NOT < -3.96

we accept phi3 (null hypothesis : there's a unit root AND no-trend) because 5.1012 is not > 6.09

we accept phi2 (null hypothesis : there is a unit root without trend and without drift) because 3.6559 is not > 8.27