Hi Ajay: That's a good point. It's really a maximization of the sum of the likelihoods of the individual series if you assume independent shocks. I'd have to look inside arima ( when I got the courage ),<br />extract the likelihood piece and then put ithe sum inside say optim That's why I was kind of hoping there might be something out there , even if independence needed to be assumed.<br /><br />But, I don't think your idea is quite equivalent to the DLM approach because there you are able to<br />specify correlation structure on the multiple series rather than assuming independence of each series. For my problem, I have no idea whether relaxing the assumption as your idea would do, would matter ? All these things are approximations to reality anyway so who ever knows ?<br /><br />I'll I either go the DLM route ( spencer mentioned that I should also look at Pinheiro and Bates ) or your route but I'm not there yet anyway. I was just thinking about this for the down the road if and<br />when I need it and I hope that I do because that would indicate progress.<br /><br /><br /><br /><br /><br /><br /><br /><p>On May 23, 2009, <strong>Ajay Shah</strong> <ajayshah@mayin.org> wrote: </p><div class="replyBody"><blockquote style="border-left: 2px solid #267fdb; margin: 0pt 0pt 0pt 1.8ex; padding-left: 1ex">On Fri, May 22, 2009 at 08:13:25PM -0500, <a href="mailto:markleeds@verizon.net" target="_blank" class="parsedEmail">markleeds@verizon.net</a> wrote:<br />> Hi everyone: Normally, if one has a single realization of a time series and one wants to estimate <br />> say an ARMA(p,q) , where p and q are known ( for simplicity ) then one estimates it and that's that. <br />> <br />> 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. <br /><br />Could we perhaps think of this as follows.<br /><br />We are holding two realisations from the same process:<br /> x1, x2, ... xN<br /> y1, y2, ... yN<br /><br />and let's suppose these two realisations are completely<br />independent. Think of two parallel experiments running with the<br />identical data generating process but a different set of random<br />shocks.<br /><br />Then you could construct the overall log likelihood of what you have<br />observed as logl(theta; x) + logl(theta; y) and maximise that.<br /><br />Is there an existing R function off the shelf which yields the ARMA<br />log likelihood? If so then it should be easy to put together an<br />overall logl() function for this problem which can be then given to<br />optim() to do estimation.<br /><br />-- <br />Ajay Shah <a href="http://www.mayin.org/ajayshah" target="_blank" class="parsedLink">http://www.mayin.org/ajayshah</a> <br /><a href="mailto:ajayshah@mayin.org" target="_blank" class="parsedEmail">ajayshah@mayin.org</a> <a href="http://ajayshahblog.blogspot.com" target="_blank" class="parsedLink">http://ajayshahblog.blogspot.com</a><br /><*(:-? - wizard who doesn't know the answer.<br /></blockquote></div>