Which one is better?

KAUSHIK BHATTACHARJEE a ?crit :

I have some time series .more than 1000 observations each ..I want to 
test if  they contain unit roots...
I am performing ADF as well as  KPSS tests...I am getting contraditory 
results in 7 out of 10 series....KPSS test is rejecting stationarity 
where as ADF test is not....
Which one is more reliable test...any idea/reference?
 
  

any reference? Yes, the paper of KPSS! It is not too technical and in 
the empirical part they discuss this issue of contradictory results with 
unit roots tests (if I remember well there are five cases from the 
Nelson Plosser data were KPSS is different than ADF, so that's a known 
issue:-).

I would rather base on a unit root test (btw rather ERS than ADF) as the 
KPSS test is rather considered as a "confirmatory test". Base on unit 
root tests especially when both tests are rejected, as unit root tests 
are known to have low power and rejection is then a pretty "big sign". 
But note that their size is not so good neither, while KPSS can have 
really big size distortions, try yourself:

library(urca)

simul.cval<-function(ar, n=100){
 series<-arima.sim(model=list(ar=ar), n=n)
 summary(ur.kpss(series, use.lag=1))@teststat
}

mc<-replicate(500, simul.cval(ar=0.2))
mean(mc>  0.463)

mc<-replicate(500, simul.cval(ar=0.9))
mean(mc>  0.463)

Hope this helps

Mat

Kaushik Bhattacharjee



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