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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")) })

resADFaic

(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.

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  • $\begingroup$ 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. $\endgroup$ – Christoph Hanck Dec 7 '18 at 9:55
  • $\begingroup$ How would you infer the unit root given the lags above then? $\endgroup$ – Alexander Butler Dec 7 '18 at 16:08
  • $\begingroup$ 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? $\endgroup$ – Christoph Hanck Dec 7 '18 at 16:42
  • $\begingroup$ 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. $\endgroup$ – Alexander Butler Dec 7 '18 at 17:19
  • $\begingroup$ "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. $\endgroup$ – Christoph Hanck Dec 7 '18 at 17:28

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