Solved – ADF test in R using adf.test vs ur.df

augmented-dickey-fullerrstationarityunit root

In the following result, the adf.test shows that the series is non stationary, while ur.df shows it is stationary (choose the lags based on decreasing from lags=5 until the lag coefficient becomes significant).

Should I trust that the series is stationary based on a=5% since the p value of z.lag.1 in ur.df is 0.0299<0.05?

adf.test(resid(fit1), alt='s')

Augmented Dickey-Fuller Test

data: resid(fit1)
Dickey-Fuller = -1.6595, Lag order = 3, p-value = 0.7089
alternative hypothesis: stationary

summary(ur.df(resid(fit1),lags=2))

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Augmented Dickey-Fuller Test Unit Root Test #

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Test regression none 

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

Residuals:
     Min       1Q   Median       3Q      Max 
-4944058 -1028037  -388697   847454  4089084 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
z.lag.1      -0.4614     0.2047  -2.254   0.0299 *

z.diff.lag1  -0.1785     0.1808  -0.987   0.3295  

z.diff.lag2  -0.3309     0.1527  -2.167   0.0364 *

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

Residual standard error: 1762000 on 39 degrees of freedom
Multiple R-squared:  0.4053,    Adjusted R-squared:  0.3596 
F-statistic:  8.86 on 3 and 39 DF,  p-value: 0.0001328


Value of test-statistic is: -2.2543 

Critical values for test statistics: 
      1pct  5pct 10pct
tau1 -2.62 -1.95 -1.61

Best Answer

The difference is due to different DF critical values. More precisely, for adf.test, the critical value is based on the model w/. drift(intercept) term while the default ur.df statistics is based on the model w/o drift(intercept) term.

You will likely see the same result if you do summary(ur.df(resid(fit1),lags=2), type='drift')

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