[R] Output of arima

[Eric Berger]

Hi Ashim,
Per the help page for arima(), it fits an ARIMA model to the specified time
series - but the caller has to specify the order - i.e. (p,d,q) - of the
model.
The default order is (0,0,0) (per the help page). Hence your two calls are
different. The first call is equivalent to order=c(0,0,0) and the second
specifies order=c(1,0,0).
In the first, since there is no auto-regression, all the variance is
"assigned" to the innovations, hence sigma^2 = 5.233.
The second case you understand.
A clue that this was happening is that the first call only returns a single
coefficient (where is the autoregressive coefficient? - not there because
you didn't ask for it).
The second call returns two coefficients, as requested/expected.

HTH,
Eric


On Wed, Nov 14, 2018 at 12:08 PM Ashim Kapoor <ashimkapoor using gmail.com> wrote:

> Dear Eric and William,
>
> Why do the 1st and 2nd incantation of arima return sigma^2 as 5.233 vs
> .9999?
> The help for arima says  --->  sigma2: the MLE of the innovations variance.
> By that account the 1st result is incorrect. I am a little confused.
>
> set.seed(123)
> b <- arima.sim(list(order = c(1,0,0),ar= .9),n=1000000,sd=1)
>
> # Variance of the innovations, e_t = 1
>
> # Variance of b = Var(e_t)/(1-Phi^2) = 1 / (1-.81) = 5.263158
>
> arima(b)
>
> > arima(b)
>
> Call:
> arima(x = b)
>
> Coefficients:
>       intercept
>         -0.0051
> s.e.     0.0023
>
> sigma^2 estimated as 5.233:  log likelihood = -2246450,  aic = 4492903
> >
>
>
> arima(b,order= c(1,0,0))
>
> Call:
> arima(x = b, order = c(1, 0, 0))
>
> Coefficients:
>          ar1  intercept
>       0.8994    -0.0051
> s.e.  0.0004     0.0099
>
> sigma^2 estimated as 0.9999:  log likelihood = -1418870,  aic = 2837747
> >
>
> On Tue, Nov 13, 2018 at 11:07 PM William Dunlap <wdunlap using tibco.com> wrote:
>
> > Try supplying the order argument to arima.  It looks like the default is
> > to estimate only the mean.
> >
> > > arima(b, order=c(1,0,0))
> >
> > Call:
> > arima(x = b, order = c(1, 0, 0))
> >
> > Coefficients:
> >          ar1  intercept
> >       0.8871     0.2369
> > s.e.  0.0145     0.2783
> >
> > sigma^2 estimated as 1.002:  log likelihood = -1420.82,  aic = 2847.63
> >
> >
> > Bill Dunlap
> > TIBCO Software
> > wdunlap tibco.com
> >
> > On Tue, Nov 13, 2018 at 4:02 AM, Ashim Kapoor <ashimkapoor using gmail.com>
> > wrote:
> >
> >> Dear All,
> >>
> >> Here is a reprex:
> >>
> >> set.seed(123)
> >> b <- arima.sim(list(order = c(1,0,0),ar= .9),n=1000,sd=1)
> >> arima(b)
> >>
> >> Call:
> >> arima(x = b)
> >>
> >> Coefficients:
> >>       intercept
> >>          0.2250
> >> s.e.     0.0688
> >>
> >> sigma^2 estimated as 4.735:  log likelihood = -2196.4,  aic = 4396.81
> >> >
> >>
> >> Should sigma^2 not be equal to 1 ? Where do I misunderstand ?
> >>
> >> Many thanks,
> >> Ashim
> >>
> >>         [[alternative HTML version deleted]]
> >>
> >> ______________________________________________
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> >> PLEASE do read the posting guide
> >> http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained, reproducible code.
> >>
> >
> >
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.
>

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