# Alternative Hypothesis for ADF Test

I'd like to conduct an augmented dickey fuller test to test my time series for unit root (against the alternative hypothesis of stationarity). Until now I did the following test:

summary(ur.df(na.omit(ApplStock),type = c("drift"), selectlags = c("AIC")))


and get this result:

###############################################
# Augmented Dickey-Fuller Test Unit Root Test #
###############################################

Test regression drift

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

Residuals:
Min        1Q    Median        3Q       Max
-0.068892 -0.003080 -0.000101  0.003238  0.036876

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.409e-05  4.143e-04  -0.058 0.953659
z.lag.1     -8.140e-01  5.643e-02 -14.424  < 2e-16 ***
z.diff.lag   1.674e-01  4.779e-02   3.503 0.000509 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.00858 on 426 degrees of freedom
Multiple R-squared:  0.3668,    Adjusted R-squared:  0.3638
F-statistic: 123.4 on 2 and 426 DF,  p-value: < 2.2e-16

Value of test-statistic is: -14.4241 104.0291

Critical values for test statistics:
1pct  5pct 10pct
tau2 -3.44 -2.87 -2.57
phi1  6.47  4.61  3.79


As far as I know, I can reject the null of unit root for all significance levels. But for which alternative hypothesis? Can someone help me with the interpretation? Any help is highly appreciated. Thank you very much.

Your test statistic involves the quantity $(\rho-1)$. If the value of the statistic is negative, it indicates that $\rho<1$, and so you are rejecting the null of a unit root with statistical evidence that $\rho <1$ and so that that process is stationary.

If you had obtained a positive value for the statistic and it was to the far right tail of the distribution under the null, it would be an indication for an explosive series.

• Thank you very much Alecos Papadopoulos. I always thought that when the test statistics (-14.4241) is less than the 1pct tau2 value (-3.44) I can reject the null of unit root for the alternative hypothesis of stationary on the 99% significance level. Otherwise, if (-14.4241) was above the (-3.44) I could not reject the null of unit root. Is that interpretation wrong? – user144267 Jan 24 '17 at 15:51
• @user144267 It is correct. – Alecos Papadopoulos Jan 24 '17 at 15:53
• Great, I highly appreciate you help! Thank you very much! – user144267 Jan 24 '17 at 15:55
• You're welcome. Please don't forget to accept my answer so that your question leaves the "unanswered" queue. – Alecos Papadopoulos Jan 24 '17 at 15:56
• Great, thanks a lot! I erased my previous comment (and will erase this one too later.) – amoeba says Reinstate Monica Jan 28 '17 at 22:03