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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)?

Saraz
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1 Answers1

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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

yonderkens
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  • 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 there is a unit root. Is that correct? – Saraz May 30 '19 at 20:47
  • 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. – yonderkens May 31 '19 at 00:15
  • Refer to this post, similar question asked here. https://stats.stackexchange.com/questions/251557/interpretation-of-ur-df-output-in-r-dickey-fuller-test-package-urca – yonderkens May 31 '19 at 00:16
  • I was missing the "absolute" value. Thank you for clarification. – Saraz May 31 '19 at 00:57
  • regarding the large values of test statistics, are they indicating something? What can cause such large values? I suspected the number of lags, but get even larger values (-23.2774 180.613 270.9181) when I use the AIC/BIC for lag selection. – Saraz May 31 '19 at 01:14
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    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. – yonderkens May 31 '19 at 14:00
  • So by themselves they indicate nothing, in relation to critical values they indicate whether you would be risky in rejecting that null, and that's about it. For lag selection in a stationary time series model, I look at ACF and PACF plots, I've never come across using AIC/BIC to choose lags but that doesn't mean it's not possible, haven't looked into it! – yonderkens May 31 '19 at 14:03
  • thank you for explaining the relation between test stat and p-value. I asked a question regarding KPSS in this post (https://stats.stackexchange.com/questions/411077/kpss-difference-between-level-stationary-and-trend-stationary) and I appreciate your advise on it. – Saraz Jun 01 '19 at 00:55
  • No problem, glad to help out – yonderkens Jun 01 '19 at 01:33