[R] unexpected result from KalmanRun (KalmanLike, StructTS)
charles_loboz at yahoo.com
Wed Nov 30 23:12:05 CET 2005
(re-formulate, re-send, without html)
for vector y = c(1,2,3,4,5), H = 0.66 manual
using the equations below give a =
KalmanRun with these parameters gives res$states =
for Kalman Filter Durbin/Koopman give at p67 eqs
v = y - Z a, F = Z P Z' + H, K = T P Z' / F +
a[t+1] = T a + K v, P[t+1] = T P L' + R Q R'
for P1 = 0, Q=0, T=Z=R=1 that reduces to:
v = y - a, F = H, K = H, a[t+1] = a + K v,
P[t+1] = 0
(also equivalent to exponential moving average,
So I am getting a serious discrepancy between manual
and KalmanRun computations. To make things more
interesting, looking into the code of arima.c we have
at line 109 an equivalent of
a[t+1] = anew + Pnew * resid0 / gain
where gain = mod$h = H (by line 97), resid0 = y-a =
v (by lines 94-96)
Since Pnew = 0, then a[t+1] = a, which explains why
returns res$states = c(1,1,1,1,1).
The help file says "'states', the contemporaneous
which I assumed to mean 'a' in the equations above.
assumption does not agree with the numerical
results. It also
does not agree with the coding(?) as a[t+1] = a + K
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?
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