R help - May 2005 - Trying to understand kpss.test() in tseries package

I'm trying to understand how to use kpss.test() properly.  If I have a
level stationary series like rnorm() in the help page, shouldn't I get a
small p-value with the null hypothesis set to "Trend"?  The
(condensed)
output from kpss.test() for the two possible null hypotheses is given
below.  I don't see any significant difference between these results.  
> x <- rnorm(1000)  # is level stationary
> kpss.test(x, null="Level")
        KPSS Test for Level Stationarity
KPSS Level = 0.0638, Truncation lag parameter = 7, p-value = 0.1
Warning:  p-value greater than printed p-value
> kpss.test(x, null="Trend")
        KPSS Test for Trend Stationarity
KPSS Trend = 0.0275, Truncation lag parameter = 7, p-value = 0.1
Warning:  p-value greater than printed p-value

I can't get the original reference easily.

Scott Waichler
Pacific Northwest National Laboratory
scott.waichler at pnl.gov

On Mon, 02 May 2005 14:43:02 -0700 Waichler, Scott R wrote:
> 
> I'm trying to understand how to use kpss.test() properly.  If I have a
> level stationary series like rnorm() in the help page, shouldn't I get
> a small p-value with the null hypothesis set to "Trend"?
No, every level stationary series is also trend stationary (with a zero
trend). Hence, the test statistic is even smaller for null = "Trend"
because first the trend is removed (which is not exactly zero due to
random variation).
Z
>  The (condensed)
> output from kpss.test() for the two possible null hypotheses is given
> below.  I don't see any significant difference between these results. 
> 
> 
> > x <- rnorm(1000)  # is level stationary
> > kpss.test(x, null="Level")
>         KPSS Test for Level Stationarity
> KPSS Level = 0.0638, Truncation lag parameter = 7, p-value = 0.1
> Warning:  p-value greater than printed p-value
> 
> > kpss.test(x, null="Trend")
>         KPSS Test for Trend Stationarity
> KPSS Trend = 0.0275, Truncation lag parameter = 7, p-value = 0.1
> Warning:  p-value greater than printed p-value
> 
> I can't get the original reference easily.
> 
> Scott Waichler
> Pacific Northwest National Laboratory
> scott.waichler at pnl.gov
> 
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