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