[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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