Interpretation of ur.df output in R , Dickey-Fuller Test package urca 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 accepted since the test-statistic 5.1012 < 6.25 critique value and phi2 is accepted
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
 A: You are right! In ADF package urca you just have to take into consideration:  
1) type="none": delta y(t) = gamma * y(t-1) + e(t)
tau1: Ho: gamma = 0 (unit root) 
2) type="drift": delta y(t) = a0 + gamma * y(t-1) + e(t)
tau2: Ho: gamma=0 (unit root).
phi1: combined Ho:  gamma = a0 = 0 (unit root and no drift). Rejecting this null implies that one OR two was NOT zero.  
3) type="trend": delta y(t) = a0 + gamma * y(t-1) + a2(t) + e(t)
tau3: Ho: gamma=0 (unit root)
phi3: gamma = a2 = 0 (unit root AND no trend at same time). Rejecting this null implies that one OR two was NOT zero.
phi2: Ho: gamma = a0 = a2 = 0.(unit root, no drift term AND no time trend term).   Rejecting this null implies that one, two, OR all three of these terms was NOT zero.  
Once you know the null hypothesis, you have to compare value of "test-statistic" with value of "critical value". To reject the null hypothesis test-statistic has to be more extreme than critical value.
I usually take 5pct critical value to study econometric time series. 
