> Subject: [R] LRT in arima models > Date: Mon, 17 Feb 2003 11:53:04 +0100 > From: "vito muggeo" <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > > 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
Just a general comment: I am more surprised that the test is still doing that well: An AR coefficient of 0.7 introduces quite a bit of dependence in your DGP. Hence the number of "independent observations" is considerably smaller than 100. Therefore asymptotic theory might be a bad approximation and small sample effects might lead to severe size distortions. Maybe someone can explain more formally whats going on here? best Adrian -- Dr. Adrian Trapletti Phone : +41 (0) 1 994 5631 Trapletti Statistical Computing Mobile: +41 (0)76 370 5631 Wildsbergstrasse 31 Fax : +41 (0) 1 994 5631 CH-8610 Uster Email : mailto:[EMAIL PROTECTED] Switzerland WWW : http://trapletti.homelinux.com ______________________________________________ [EMAIL PROTECTED] mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-help
