adf.test.help

Thanks Matthieu: I agree with you but his series is actually normal with
E(X) = 0 and rho_i = 0 for all i so it is mean reverting but
not even reverting.in the sense of being dependent on itdself.? It's just
there at zero all the time.

I think the series I asked him to construct is a dumb example but it is one
of those series that doesn't have a unit root and is not mean reverting. So,
I think it's just an issue of terminology because usually when these terms
are being used, they are used in the context? series is dependent on
previous values of itself. In Arnaud's case, this wasn't the case. Thanks
for your explanation.

Arnaud: If you want to say that a series that doesn't have a unit root? is
stationary, I guess it's okay because the use of the terms
can be tricky. I'm sorry if I was being too picky.






On Feb 17, 2010, mat <matthieu.stigler at gmail.com> wrote:

Well I would say yes, but I'm sure you can find some paper where the
authour finds a process that is stationary but not mean-reverting....

Weak stationarity is defined as the existence of (asymptotically)
time-invariant expectation and auto-covariance, so this will generally
mean your process will be mean reverting.

At least an AR(q) process that has roots lying outside the unit circle
is mean reverting, and this is what you are estimating.

Hope this helps, and hope I'm not too wrong...

Mat
Arnaud Battistella a ?crit :

Thanks, so do you confirm that a stationary series is *always*
mean-reverting?

-Arnaud


On Wed, Feb 17, 2010 at 7:10 PM, mat <matthieu.stigler at gmail.com> wrote:

Arnaud Battistella a ?crit :

Hi,

I am trying to test whether a return series is stationary, but before
proceeding I wanted to make sure I understand correctly how to use the
adf.test function and interpret its output... Could you please 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)
adf.test(x, "stationary", k=0)

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?

yes

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.

yes

Thanks,

-Arnaud