[R] AR vs ARIMA question

[Bert Gunter]

WARNING: The following might be **complete baloney** (and my apologies if so).

Erin:
I hope you get a definitive reply on this from a real expert, but if
memory serves, they might be using two different estimation
algorithms. ar() is just doing Yule-Walker recursive calculation as
described in Box-Jenkins, while arima() is using numerical
optimization. You can probably make them closer by changing
convergence criteria for arima(), which would be a good test for my
"explanation."

Cheers,
Bert



On Thu, Jul 7, 2011 at 7:36 AM, Erin Hodgess <erinm.hodgess at gmail.com> wrote:
> Dear R People:
>
> Here is some output from AR and ARIMA functions:
>
>> xb <- arima.sim(n=120,model=list(ar=0.85))
>> xb.ar <- ar(xb)
>> xb.ar
>
> Call:
> ar(x = xb)
>
> Coefficients:
>     1
> 0.6642
>
> Order selected 1  sigma^2 estimated as  1.094
>> xb.arima <- arima(xb,order=c(1,0,0),include.mean=FALSE)
>> xb.arima
>
> Call:
> arima(x = xb, order = c(1, 0, 0), include.mean = FALSE)
>
> Coefficients:
>         ar1
>      0.6909
> s.e.  0.0668
>
> sigma^2 estimated as 1.04:  log likelihood = -172.94,  aic = 349.88
>>
>
> My question:  shouldn't the ar1 and arima coefficients and sigma^2 be
> the same, please?  Or at least closer than they are?
>
>
>
> Thanks,
> Erin
>
>
> --
> Erin Hodgess
> Associate Professor
> Department of Computer and Mathematical Sciences
> University of Houston - Downtown
> mailto: erinm.hodgess at gmail.com
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>



-- 
"Men by nature long to get on to the ultimate truths, and will often
be impatient with elementary studies or fight shy of them. If it were
possible to reach the ultimate truths without the elementary studies
usually prefixed to them, these would not be preparatory studies but
superfluous diversions."

-- Maimonides (1135-1204)

Bert Gunter
Genentech Nonclinical Biostatistics