[R-SIG-Finance] adf.test.help

[Arnaud Battistella]

Mark, indeed, the series you gave me doesn't have a unit root
(adf.test confirms this) but is clearly not mean reverting. I assume
we cannot say that this series is stationary, or maybe on restricted
segments... How would you test such series?
Matthieu, thanks a lot for this explanation, that makes things clearer
to me, I just wanted to make sure I was not overlooking something that
could pose me problems later on.

Arnaud


On Wed, Feb 17, 2010 at 7:55 PM,  <markleeds at verizon.net> wrote:
> 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 écrit :
>> 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 écrit :
>>>
>>>> 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
>>>>
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>>>
>
>