adf.test.help

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?

  

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

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

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