Kalman filter for general state space models, especially in its naive version, is known for its numerical instability. This is the reason why people developed square root filters, based on Cholesky decomposition of variance matrices. In package dlm the implementation of Kalman filter is based on the singular value decomposition (SVD) of the relevant variance matrices, providing for a more robust algorithm than the standard square root filter.
The lack of convergence of optimization algorithms in finding MLEs of unknown parameters is not surprising to me, especially if you have many parameters. When using state space models it is easy to end up with a fairly flat, or multimodal likelihood function. These are two signs of poor identifiability of the model. You can live with it, but be aware that it is there. My suggestion is to start the optimization from several different initial values and compare maximized values of the likelihood. Simulated annealing may be used to better explore the parameter space. HTH, Giovanni > Date: Thu, 15 Nov 2007 04:41:26 +0000 (GMT) > From: [EMAIL PROTECTED] > Sender: [EMAIL PROTECTED] > Priority: normal > Precedence: list > > Hi, > > Following convention below: > y(t) = Ax(t)+Bu(t)+eps(t) # observation eq > x(t) = Cx(t-1)+Du(t)+eta(t) # state eq > > I modified the following routine (which I copied from: > http://www.stat.pitt.edu/stoffer/tsa2/Rcode/Kall.R) to accommodate u(t), an > exogenous input to the system. > > for (i in 2:N){ > xp[[i]]=C%*%xf[[i-1]] > Pp[[i]]=C%*%Pf[[i-1]]%*%t(C)+Q > siginv=A[[i]]%*%Pp[[i]]%*%t(A[[i]])+R > sig[[i]]=(t(siginv)+siginv)/2 # make sure sig is symmetric > siginv=solve(sig[[i]]) # now siginv is sig[[i]]^{-1} > K=Pp[[i]]%*%t(A[[i]])%*%siginv > innov[[i]]=as.matrix(yobs[i,])-A[[i]]%*%xp[[i]] > xf[[i]]=xp[[i]]+K%*%innov[[i]] > Pf[[i]]=Pp[[i]]-K%*%A[[i]]%*%Pp[[i]] > like= like + log(det(sig[[i]])) + t(innov[[i]])%*%siginv%*%innov[[i]] > } > like=0.5*like > list(xp=xp,Pp=Pp,xf=xf,Pf=Pf,like=like,innov=innov,sig=sig,Kn=K) > } > > I tried to fit my problem and observe that I got positive log likelihood > mainly because the log of determinant of my variance matrix is largely > negative. That's not good because they should be positive. Have anyone > experience this kind of instability? > > Also, I realize that I have about 800 sample points. The above routine when > being plugged to optim becomes very slow. Could anyone share a faster way to > compute kalman filter? > > And my last problem is, optim with my defined feasible space does not > converge. I have about 20 variables that I need to identify using MLE method. > Is there any other way that I can try out? I tried most of the methods > available in optim already. They do not converge at all...... Thank you. > > - adschai > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- Giovanni Petris <[EMAIL PROTECTED]> Department of Mathematical Sciences University of Arkansas - Fayetteville, AR 72701 Ph: (479) 575-6324, 575-8630 (fax) http://definetti.uark.edu/~gpetris/ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
