From: charles loboz <charles_loboz_at_yahoo.com>

Date: Thu 01 Dec 2005 - 09:12:05 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Dec 01 09:32:06 2005

Date: Thu 01 Dec 2005 - 09:12:05 EST

(re-formulate, re-send, without html)

for vector y = c(1,2,3,4,5), H = 0.66 manual
calculations

using the equations below give a =

c(1,1.66,2.55,3.51,4.50).

KalmanRun with these parameters gives res$states =

(1,1,1,1,1)!

for Kalman Filter Durbin/Koopman give at p67 eqs 4.13:

v = y - Z a, F = Z P Z' + H, K = T P Z' / F + H,

a[t+1] = T a + K v, P[t+1] = T P L' + R Q R'

for P1 = 0, Q=0, T=Z=R=1 that reduces to:

v = y - a, F = H, K = H, a[t+1] = a + K v, P[t+1] = 0

(also equivalent to exponential moving average, Durbin/Koopman p49)

So I am getting a serious discrepancy between manual and KalmanRun computations. To make things more interesting, looking into the code of arima.c we have at line 109 an equivalent of

a[t+1] = anew + Pnew * resid0 / gain
where gain = mod$h = H (by line 97), resid0 = y-a =
v (by lines 94-96)

Since Pnew = 0, then a[t+1] = a, which explains why
the computation

returns res$states = c(1,1,1,1,1).

The help file says "'states', the contemporaneous
state estimates",

which I assumed to mean 'a' in the equations above.
But that

assumption does not agree with the numerical
results. It also

does not agree with the coding(?) as a[t+1] = a + K
v differs

substantially from a[t+1] = anew + Pnew * resid0 /
gain. (all the previous lines of coding follow the
kalman filter equations, but this one does not seem to
- do we have some strong reformulation of the
equations in the basic form?).

So, what does 'states' contain?

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Dec 01 09:32:06 2005

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