[R-SIG-Finance] time series question

[spencerg]

      The "lme" function maximizes a likelihood specified by the model 
implicit in the formula. 


      If you are worried about a lack of normality, I suggest that 
before you do a lot of work to invent your own thing, you try "lme", and 
plot residuals, estimated coefficients using "coef.lme", etc.  If you 
see evidence that the normal likelihood is not adequate, you would then 
have justification for doing something more complicated. 


      Spencer Graves    

markleeds at verizon.net wrote:
> 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 ),
> 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.
>
> But,  I don't think your idea is quite equivalent to the DLM approach because 
> there you are able to
> 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 ?
>
> 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
> when I need it and I hope that I do because that would indicate progress.
>
>
>
>
>
>
>
> On May 23, 2009, *Ajay Shah* <ajayshah at mayin.org> wrote:
>
>     On Fri, May 22, 2009 at 08:13:25PM -0500, markleeds at verizon.net
>     <mailto: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 <mailto:ajayshah at mayin.org> http://ajayshahblog.blogspot.com
>     <*(:-? - wizard who doesn't know the answer.
>
>   
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