[R-SIG-Finance] time series question

[Ajay Shah]

On Fri, May 22, 2009 at 08:13:25PM -0500, markleeds at verizon.net wrote:
> Hi everyone: Normally, if one has a single realization of a time series and one wants to estimate 
> say an ARMA(p,q) , where p and q are known ( for simplicity )  then one estimates it and that's that. 
> 
> But, suppose that one has more than one realization  of the time series ( assuming each series is the same length) and yet still wants to estimate the "best" arma(p,q) , over all the realizations,  again where p and q are known. 

Could we perhaps think of this as follows.

We are holding two realisations from the same process:
   x1, x2, ... xN
   y1, y2, ... yN

and let's suppose these two realisations are completely
independent. Think of two parallel experiments running with the
identical data generating process but a different set of random
shocks.

Then you could construct the overall log likelihood of what you have
observed as logl(theta; x) + logl(theta; y) and maximise that.

Is there an existing R function off the shelf which yields the ARMA
log likelihood? If so then it should be easy to put together an
overall logl() function for this problem which can be then given to
optim() to do estimation.

-- 
Ajay Shah                                      http://www.mayin.org/ajayshah  
ajayshah at mayin.org                             http://ajayshahblog.blogspot.com
<*(:-? - wizard who doesn't know the answer.