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

[mat]

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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>>