Arnaud Battistella arnaudb25 at gmail.com
Wed Feb 17 18:14:06 CET 2010

```Hi,

I am trying to test whether a series is return series stationary, but
before proceeding I wanted to make sure I understand correctly how to
let me know whether I am correct in my interpretations?

ex: I take x such as I know it doesn't have a unit root, and is
therefore stationary

1/
> x <- rnorm(1000)

Augmented Dickey-Fuller Test

data:  x
Dickey-Fuller = -31.8629, Lag order = 0, p-value = 0.01
alternative hypothesis: stationary

Warning message:
In adf.test(x, "stationary", k = 0) : p-value smaller than printed p-value

If I understand correctly, I am told that the probability of x having
a unit root and therefore being non-stationary is 0.01, so the test
tells me that there is a very high probability that x is stationary.
Then I can conclude that x is mean-reverting. Am I correct?

2/ I would like to see critical values also, so I tried with ur.df

> summary(ur.df(x, "trend", lag=0))

<snip>

Value of test-statistic is: -31.8629 338.4156 507.6231

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

Here if I understand correctly, as my first critical value is
significantly less than the 1% critical value I reject the null
hypothesis that x has a unit root, so x is stationary and then mean
reverting.

Thanks,

-Arnaud

```