I am having trouble with interpreting the Dickey-Fuller test on a time series using the ur.df() function in the urca package. I already read this thread but still need some advise.

The command is: My_TS %>% ur.df(type = "trend") %>% summary() The R output is: enter image description here

What I understand is "tau3" is the gamma=0 null hypothesis. The first test statistic = -23.2774 is within the region of rejecting the null, implying a unit root is not present. Please correct me if I am wrong.
I also know (from the above mentioned post) failing to reject phi3 implies two things :

  • gamma = 0 (unit root) AND
  • there is no time trend term.

Failing to reject phi2 implies:

  • gamma = 0 AND
  • no time trend term AND
  • no drift term.

I am not sure what are the 180.613 270.9181 values. Are they test statistics for phi2 and phi3 respectively? and if these large values indicating something? If above values are t-statistics of phi2 and phi3 then I fail to reject the h0 concluding a unit root,no trend no drift. Isn't it contradictory with tau3 value that implies no unit root?

  • $\begingroup$ I figured out part of the answers: 1) always compare the absolute values of test statistic with absolute value of critical values. 2) phi2 test stat is 180.613 and phi2 h0 is rejected as test stat > phi2 critical values. The reason to get these large test stats are still unclear though! $\endgroup$ – Saraz May 31 at 1:07

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