ARIMA simulation including a constant

Tue, Jan 4, 2011 5:05 AM

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

ARIMA simulation including a constant

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