[R] LRT in arima models

[vito muggeo]

Dear all,

For some reason I'm evaluating the size of the LRT testing for the effect of
some explanatory variable in arima models.
I performed three different simulations
y<-2+arima.sim(n, model=list(ar=ar.p,ma=0),sd=1)
with different ar parameter, namely 0.7, 0.5, and 0.2. n=100.

Out of 1000 replications performed for each ar, the H_0 (no effect of
x<-1:n) was rejected 77, 67 and 53 times with ar=0.7, 0.5 and 0.2
respectively. (sigma was assumed known in calculating the statistic test and
the nominal significance level is 0.05)

That is, the LRT seems to become somewhat anti-conservative when the ar
parameter increases.
I am aware the 1000 replictions are few to assess the size, but the "trend"
in the sizes seems noticeable.  Am I wrong?
Am I missing some theoretical issues or could it depend on any computational
apect related to the the arima() function?

Any comment is coming?
Many thanks
best,
vito