> Subject: [R] LRT in arima models
> Date: Mon, 17 Feb 2003 11:53:04 +0100
> From: "vito muggeo" <vito.muggeo at giustizia.it>
> To: <r-help at stat.math.ethz.ch>
>
> 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
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