[R] AR vs ARIMA question

[Prof Brian Ripley]

Yes, ar and arima are using different estimation methods: arima is mle 
whereas the default is method-of-moments.

With such a large ar coefficient the end effects will matter, and the 
mle (done by arima or ar.mle or ar(method="mle")) is the more accurate 
method since it makes maximal use of the ends of the series.

Using coda (and set.seed(1)):

> effectiveSize(as.mcmc(xb))
   var1
8.3611

so you have effectively about 8 independent samples and your estimates 
(by whatever method) have high variability.   Take a much longer 
series.

On Thu, 7 Jul 2011, Bert Gunter wrote:

> 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.
>>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595