R help - Jun 2011 - How to reconcile Kalman filter result (by package dlm) with linear regression?

 
Hello All,
 
I am working with dlm for the purpose of estimating and forecasting with a
Kalman filter model. I have succesfully set up the model and started generating
results. Of course, I need to somehow be sure that the results make sense.
Without any apparent target to compare with, my natural selection is the results
by odinary least square. The idea being that if I choose a diffuse prior, the
result should approach whatever results that lm() would generates.
 
However, the results turns out to be very different, even though the signs of
the estimates coincide. Linear regression gives the following results
 
lm1 = lm(Y~0+X)
#########################################################
#> lm1$coef
# XV1 XV2 XV3 XV4 
#-0.008293796 0.002183550 -0.004053199 0.003030834 
#########################################################
 
and Kalman filter generate this set of results:
> m
             [,1]        [,2]        [,3]       [,4]
[24,] -0.06046868 0.002829377 -0.01569903 0.03599957
 
I am pretty troubled by what I see here. So if anyone would offer me some
condolence, as well as helpful advice, I am greatly grateful. Thanks a lot. Here
are the code and the data.
 
Thanks a lot.
 
Wei 
 
nTotal = nMatrix + 1
BuildMod <- function(x){
 L1 = matrix(0,nFactor,nFactor) 
 L1[upper.tri(L1,T)] <- x[1:nMatrix]
 return(dlm(
  m0  = rep(0,nFactor),
  C0  = diag(nFactor)*10,
  FF  = matrix(1,1,nFactor),
  GG  = diag(nFactor),
  V   = tail(x,1)^2,
  W   = crossprod(L1),
  JFF = matrix(1:4,nr=1),
  X   = X
  ))
}
ModFit  <- dlmMLE(Y,rep(0.1,nTotal),BuildMod,debug=T)
dlmMod  <- BuildMod(ModFit$par)
V  = dlmMod$V
W  = dlmMod$W
m0 = dlmMod$m0
C0 = dlmMod$C0
ModFilt <- dlmFilter(Y,dlmMod)
v <- tail(dlmSvd2var(ModFilt$U.C,ModFilt$D.C),1)
m <- tail(ModFilt$m,1)

 
Here is the value of Y:
0.0125678739370109
-0.00241285475528163
0.00386919876129071
-0.00352839097011217
0.00285344714211614
0.00374266510625097
0.00797807743013259
-0.00543459628953192
-0.0138447399853609
-0.0102614592879934
-0.0225111772602310
-0.0127304918143123
-0.00730849659351113
-0.0206703167742092
0.0228898867615212
-0.000489089315662759
0.00760340725359960
-0.0138647393981477
-0.00919507833321138
-0.00471195180636822
-0.0146605156203797
-0.00827583539820271
-0.0249602009928649

 
The value of X is a 23 by 4 matrix, values are seperated by a space. The first
column is always 1.
 
1 0.481797086735748 -0.725213272802754 1.09390587373642
1 -0.336701996049702 -0.631488034316504 1.18588655278069
1 -0.403677908907445 -0.709311690414421 1.40641758335925
1 -0.660006432637389 -0.473151167286555 1.47881106259977
1 -0.598885119922226 -0.669037137010852 1.61035313130471
1 -0.386026586737966 -0.402669473854140 1.72603754245568
1 -0.861884498592061 0.0351890847929021 1.70321193556938
1 -0.575467614543903 -0.0234300742003617 1.81371984835956
1 -1.09697129563504 -0.111460569992454 1.98698301700280
1 0.156970856187597 0.422525286064322 2.07436343379059
1 0.816563280464663 0.716962192825498 1.97867715330570
1 0.223472270913202 0.798985394320738 2.12679959513465
1 -0.901251445288375 1.08970588591384 2.31314336543201
1 0.402507298840520 0.264576256562399 2.45731905177217
1 0.655744153537491 0.745015749090142 2.46883455441981
1 1.97576880567968 2.00737408265316 2.57606000649382
1 1.05416962424537 3 2.47721380452455
1 0.128426774782304 2.85471948506395 2.29259168958684
1 0.0930179549205073 2.03239322655372 2.21711568710261
1 -0.120974956861827 0.458838879419343 1.77364638064773
1 0.446329808606182 0.873634084428291 1.65560019466879
1 1.15541338624045 1.70193933014399 1.53951603064753
1 0.658459632511477 1.42875343279004 1.55839474231335

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