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

[Arnaud Battistella]

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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>
>