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Re: How to test the regression terms in an arima model

To: <Olivier.Renaud@pse.unige.ch>
Subject: Re: How to test the regression terms in an arima model
From: Prof Brian Ripley <ripley@stats.ox.ac.uk>
Date: Tue, 3 Apr 2001 17:45:01 +0100 (BST)
Cc: Snews <s-news@wubios.wustl.edu>
In-reply-to: <3AC9F9CF.F57FEED3@pse.unige.ch>
On Tue, 3 Apr 2001 Olivier.Renaud@pse.unige.ch wrote:

> S users,
>
> > version
> S-PLUS 2000 Professional Edition Release 3 for Microsoft Windows : 2000
>
>
> When I fit an arima model with regression terms, I would like to test
> the significance of these terms. However the following call gives me the
> coefficients but not standard errors and tests:
>
> > summary (arima.mle(y, model=list(order=c(1,0,0)), xreg=cbind(1,eff)))
> ...
> Coeffficients for regressor(s): cbind(1, eff)
> [1] -0.15789  1.18306
> ...

Right. Do a likelihood ratio test (make sure n.cond is the same),
as you have the conditional likelihood in the object.

>
> Note that gls gives the tests on the regressions terms (slighly
> different values for the coefficients, since estimated with a different
> method). But for different reasons, I would prefer to stay in the arima
> framework.

gls at least does full MLE, and so is preferable.  It is often a lot
slower, though.

>
> > summary (gls (y ~ eff, correlation = corAR1())
> ...
> Coefficients:
>                 Value Std.Error   t-value p-value
> (Intercept) -0.172742 0.1019278 -1.694752  0.0909
>         eff  1.197824 0.1439301  8.322260  <.0001
> ...
>
> Any tip would be appreciated.
>
> Olivier
> --
> ----------------------------------------------------------------------
> Olivier Renaud                      mailto:Olivier.Renaud@pse.unige.ch
> Faculty of Psychology and Education               Tel: +41 22 705 9104
> University of Geneva   -   40, Bd du Pont d'Arve  -   CH-1211 Geneva 4
>                        http://www.unige.ch/fapse/PSY/persons/prof-ana/
> ---------------------------------------------------------------------
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-- 
Brian D. Ripley,                  ripley@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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