# [R] ARIMA simulation including a constant

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Jan 4 14:05:06 CET 2011

```That output is not from arima(), which is the function paired with
arima.sim().  Nor is it from arima0(), so I don't believe it is
'ouptut from R' (perhaps from a contributed package you have not
mentioned?).

With arima(), the intercept is 'm' in the notation on the help page
and not 'a' in your personal re-definition.  You can easily go from
one to the other by some trivial algebra ( a = m*(1-sum(ar)) ), but
you do need to be sure what the unstated function you use is using.

On Mon, 3 Jan 2011, Paolo Rossi wrote:

> Sorry I am not really sure I have been taht clear.
>
> I meant ARMA which is not bound to have zero mean. More precisely, suppose I
> estimate y(t) = a + by(t-1)  + e(t) + ce(t-1) , i.e. and ARMA(1,1). My
> question is how do I simulate values for yt given the values for a, b and c?
> My problem with arima.sim is that I cannot find a way to pass the value for
> the constant a.
>
> Output from  R is:
>
> Coefficient(s):
>            Estimate  Std. Error  t value Pr(>|t|)
> ar1         0.82978     0.01033   80.297  < 2e-16 ***
> ma1         0.46347     0.01548   29.942  < 2e-16 ***
> intercept  -0.02666     0.01012   -2.635  0.00841 **
> ---
> Intercept is significant and I suppose it should be used if I want simulate
> values from this ARMA(1,1)
>
>
> Thanks and Apologies for not being clear
>
> Paolo
>
>
>
>
> On 3 January 2011 16:46, Prof Brian Ripley <ripley at stats.ox.ac.uk> wrote:
> On Mon, 3 Jan 2011, Paolo Rossi wrote:
>
>       Hi,
>
>       I have been looking at arima.sim to simulate the output
>       from an ARMA model
>       fed with a normal and uncorrelated input series but I
>       cannot find a way to
>       pass an intercept / constant into the model. In other
>       words, the model input
>       in the function allows only for the AR and MA components
>       but I need to pass
>       a constant.
>
>       Can anyone help?
>
>
> Well, an ARIMA model by definition has zero mean (as the link on the
> help page for arima.sim to the exact definition tells you).  Perhaps
> you mean that (X-m) = Z follows an ARIMA model, in which case simulate
> Z and add m.  For a differenced ARIMA model it is not clear if you
> meant that you wanted an intercept for the original or differenced
> series: for the latter simply simulate the differenced series, add the
> intercept and use diffinv().
>
>       Thanks
>
>       Paolo
>
>              [[alternative HTML version deleted]]
>
>
> Please do as we asked in the posting guide and not send HTML.
>
> --
> 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
>
>
>
>

--
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
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