Hi Paul: I like your idea of subtraction but, even if alphabar and betabar
are not time varying, rather than centering around the grand means, I think
he needs to center around the respective mean at that point in time ( since
he's got it indexed by i, I think that's what OP means ). But, once OP
does that, as you pointed out,  then it can easily be recast in the state
space form. So, nice idea.


Mark



P.S: It might be better to use phi_1 and phi_2 rather than assume that both
parameters have
the same AR coefficient. Then, if the estimates are not significantly
different, you can change
them to phi later. Forcing both parameters to have the same AR coefficient
seems restrictive
to me.





On Tue, Oct 30, 2012 at 9:37 PM, Paul Teetor <paulteetor@yahoo.com> wrote:

>
>
> Seder,
>
> Your question is a little unclear, so it's not possible to give you a
> precise answer. Could you clarify your question? It's also helpful if you
> briefly describe your application -- for example, tell us what time series
> are you modeling.
>
> First, is phi a given? Or do you intend phi to be a parameter (and, hence,
> estimated by dlmMLE)?
>
> Second, are alphabar and betabar given? Or are they parameters which must
> be estimated?
>
> If alphabar, and betabar are given, I suggest recentering alpha and beta
> around alphabar and betabar: subtract alphabar from alpha, and subtract
> betabar from beta. That will greatly simplify the recursion equations for
> alpha and beta:
>
>    alpha[i,t] = phi*alpha[i,t] + W[i,1,t]
>
>    beta[i,t] = phi*beta[i,t] + W[i,2,t]
>
> These equations fit easily into the state-space paradigm of DLM, and phi
> becomes just another parameter to estimate using buildCAPM and dlmMLE.
>
> If alphabar and betabar are parameters, not givens, then the situation is
> a little more complicated: you will need to incorporate them into the G
> matrix of the DLM model and also incorporate them into buildCAPM for
> estimation by dlmMLE.
>
> By the way, are you aware that you must have abs(phi) < 1.0? Otherwise
> these equations are not mean-reverting.
>
>
> Finally, are you familiar with the Triantafyllopoulos-Montana model of
> mean-reverting spreads? Your state-space equations are very similar to
> theirs, so perhaps you could build on their work.
>
> Paul Teetor, Elgin, IL  USA
> http://quanttrader.info/public
>
>
> ________________________________
>  From: nserdar <snes1982@hotmail.com>
> To: r-sig-finance@r-project.org
> Sent: Thursday, October 25, 2012 6:22 PM
> Subject: Re: [R-SIG-Finance] Kalman Filter + DLM Package in R
>
> This is Kalman Filter random walk process code :
>
> library(dlm)
>
> buildCAPM<-function(u){
>
>     dlmModReg(rm,dV=exp(u[1]),dW=exp(u[2:3]))  # rm market
>
> }
>
> outMLE<-dlmMLE(rt,parm=rep(0,3),buildCAPM)  # rt return of indusrty
>
> mod<-buildCAPM(outMLE$par)
>
> outFilter<-dlmFilter(rt,mod)
>
> mae<-mean(abs(outFilter$f)-rt)   # MAE
>
> mse<-mean(((outFilter$f)-rt)^2) #MSE
>
> What I am asking how to modify this code as Kalman Filter Mean Reverting
>
> For example:
>
> R(it)= Alpha(it)+ Beta(it)R(mt)+ V(it)
>
> KF Mean Reverting
>
> Alpha(it)= Alphabar(i)+ phi* (Alpha(it-1)-Alphabar(i))+W(i1t)
> Beta(it)= Betabar(i)+ phi* (Beta(it-1)-Betahabar(i))+W(i2t)
>
> Regards,
> Serdar
>
>
>
>
>
> --
> View this message in context:
> http://r.789695.n4.nabble.com/Kalman-Filter-DLM-Package-in-R-tp4647470p4647474.html
> Sent from the Rmetrics mailing
>  list archive at Nabble.com.
>
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