Dickey-Fuller test interpretation (urca package)

by Saraz   Last Updated May 16, 2019 01:19 AM

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:

#########################################

Augmented Dickey-Fuller Test Unit Root Test #

#########################################

Test regression trend

Call: lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals: Min 1Q Median 3Q Max -10.7876 -2.5377 -0.4552 2.0147 19.1831

Coefficients: Estimate Std. Error t value (Intercept) 6.4106000 0.3196608 20.054 z.lag.1 -0.4886546 0.0209927 -23.277 tt 0.0000442 0.0001282 0.345 z.diff.lag 0.0150514 0.0213917 0.704 Pr(>|t|)
(Intercept) <2e-16 * z.lag.1 <2e-16 * tt 0.730

z.diff.lag 0.482

Signif. codes:
0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.791 on 2186 degrees of freedom Multiple R-squared: 0.2408, Adjusted R-squared: 0.2398 F-statistic: 231.1 on 3 and 2186 DF, p-value: < 2.2e-16

Value of test-statistic is: -23.2774 180.613 270.9181

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

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?



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