# 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

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

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

• It's probably a better question for Cross Validated than SO – Hack-R Dec 13 '16 at 17:26

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.

• Could you please explain what is the condition to accept the phi2 H0 in "type=trend"? Is it if the the test-statistic (3.6559) less than 4.68 critique value? – Saraz May 30 '19 at 6:16