# [R] estimates for e in procedure arima0() ?

Prof Brian Ripley ripley at stats.ox.ac.uk
Thu Apr 12 18:59:46 CEST 2001

```On 12 Apr 2001, Kai Arzheimer wrote:

> Dear all,
> this may be a stupid question but...
>
> The underlying model in procedure arima0 is
>
> X[t] = a[1]X[t-1] + ... + a[p]X[t-p] + e[t] + b[1]e[t-1] + ... +b[q]e[t-q]
>
> Is it possible to get an estimate of e for every point t, t-1 etc. or
> at least an estimate of the variance of e?

e is not a parameter, so you cannot estimate it.  However, its variance is
a parameter whose estimate is quoted in the standard output:

> example(arima0)

arima0> data(lh)

arima0> arima0(lh, order = c(1, 0, 0))

Call:
arima0(x = lh, order = c(1, 0, 0))

Coefficients:
ar1  intercept
0.5739     2.4133

Approx standard errors:
ar1  intercept
0.1162     0.1466

sigma^2 estimated as 0.1975:  log likelihood = -29.38,  aic = 62.76
^^^^^^^^^^^^^^^^^^^^^^^^^^^

I suspect that by `estimate of e' you mean the residuals returned in the
resid component of the fit.

> Thanks a lot in advance for any hints

Hint: read the help page, run the examples, compare the output with the
references, make sure you understand what each piece means.

--
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 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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```