# R: interpreting ur.df ADF test results

I'm running ADF test on my data to test for unit root and stationarity, trend, and to find the optimal number of lags using urca package.

my code is as follows:

> resADFaic <- lapply(InvestmentTS,function(x){ summary(ur.df(x,type="trend", selectlags = "AIC")) })


(this is to lapply the ur.df test on all variables in my data)

this test yields, for an example of one of the variables:

###############################################
# 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
-0.242639 -0.009059  0.002046  0.016602  0.065003

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.1428625  0.0627106   2.278  0.02436 *
z.lag.1     -0.0951398  0.0432642  -2.199  0.02966 *
tt          -0.0003743  0.0001349  -2.776  0.00633 **
z.diff.lag   0.0133259  0.0905665   0.147  0.88325
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.03429 on 129 degrees of freedom
Multiple R-squared:  0.05708,   Adjusted R-squared:  0.03515
F-statistic: 2.603 on 3 and 129 DF,  p-value: 0.05479

Value of test-statistic is: -2.199 2.9918 3.858

Critical values for test statistics:
1pct  5pct 10pct
tau3 -3.99 -3.43 -3.13
phi2  6.22  4.75  4.07
phi3  8.43  6.49  5.47


I am completely lost on how to interpret these results. Firstly, how do I test for the presence of a unit root (stationarity)? Secondly, how can I determine if there is trend? Finally, how do I interpret the lags? what is the tt coefficient?

I have already read: Interpretting R's ur.df (Dickey-Fuller unit root test) results and am still very much lost. Any input would be greatly appreciated.

EDIT: I have figured out the first 2 questions about unit-root and trend. I am still very much confused about the lags.

• The lags are just a device to account for short-run serial correlation in the series so as to make sure inference on the unit root property is valud. They are rarely of interest in their own right. – Christoph Hanck Dec 7 '18 at 9:55
• How would you infer the unit root given the lags above then? – Alexander Butler Dec 7 '18 at 16:08
• You need to compare the test statistic -2.199 to the critical values for tau3 - that, actually, seems to be question 1 about unit roots which you said you figured out, unless I am mistaken? – Christoph Hanck Dec 7 '18 at 16:42
• I thought that tau3 was to indicate stationarity, having nothing to do with lags? That interpretation is based on the answer linked in my question. – Alexander Butler Dec 7 '18 at 17:19
• "How would you infer the unit root given the lags above then?" relates to if there is a unit root according to the test, as far as I understand. To repeat, there is nothing to infer about the unit root property of the series from the coefficients on z.diff.lag. They just serve to control for remaining serial correlation. – Christoph Hanck Dec 7 '18 at 17:28