I am testing a time series using ADF test in urca package:

summary(ur.df(data, type = "trend", lags = 1, selectlags = "Fixed"))

Value of test-statistic is: -9.774 31.8531 47.7796

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

I know that phi2 refers to the null hypothesis that there is a unit root without trend and without drift. Could you please help me to interpret the result. Should I accept the phi2 as test statistic (31.8531) is greater than critical value (6.09 4.68 4.03)?


1 Answer 1


Since your test statistic (31.8531) is greater than the critical value at the 1% level (6.09), you can reject the null hypothesis that there is a unit root, and you can accept the possibility that the series is stationary.

tl;dr Yes

  • $\begingroup$ So, I should check the test stat with critical value. If it was greater then reject the H0. Does it apply to tau3 too? In that case since is -9.774<(-3.96 -3.41 -3.12) then accept the h0-> there is a unit root. Is that correct? $\endgroup$
    – Saraz
    May 30, 2019 at 20:47
  • $\begingroup$ When comparing test stats to critical values you generally consider what has a larger absolute value. So since |-9.774| > |-3.96| you would also reject the null in this case, which means you can accept the possibility of the alternative, there is no unit root. Also review what the different stats null hypotheses are, tau3 is null unit root, phi2 is null unit root and no trend, and phi2 is null unit root with no trend and no drift. $\endgroup$
    – yonderkens
    May 31, 2019 at 0:15
  • $\begingroup$ Refer to this post, similar question asked here. stats.stackexchange.com/questions/251557/… $\endgroup$
    – yonderkens
    May 31, 2019 at 0:16
  • $\begingroup$ I was missing the "absolute" value. Thank you for clarification. $\endgroup$
    – Saraz
    May 31, 2019 at 0:57
  • 1
    $\begingroup$ Without getting too technical, a test statistic essentially relates the probability (p-value) that you would be wrong for rejecting the null hypothesis. So as test statistics get larger, your p-values get smaller, which means you are less likely to be incorrect for rejecting the null hypothesis. However, a test statistic means nothing without the critical value to compare it to. These critical values are determined by the characteristics of the distribution, like sample size, degrees of freedom, and so on. $\endgroup$
    – yonderkens
    May 31, 2019 at 14:00

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