2009/5/27 Michel Juillard <michel.juillard@ens.fr>

On closer inspection, I don't think that the expression pointed by George in kalman_filter.m is wrong:

1. reste = smpl-t or the number of periods during which the filter is stationary. This shouldn't be larger than T-start+1

2. it is problematic (see below) but not wrong to add all the determinants at once in the last period of the stationary filter

3. I don't think this explains the difference with the C++ version of the filter and we still have to look for it.

4. it remains that the current code is very unclear and that if LIK is correct the vector lik doesn't have the correct constants on each elements.

5. I would like to simplify the code and add the correct constant to each element of the lik vector. It would be a little bit less efficient in Matlab than the current code, but I doubt it would be noticeable.
Stephane, what do you think?

Best

Michel

G. Perendia wrote:

Dear Michel

I think I found an error in Dynare Matlab kalman_filter. suite of utilities
which affects the likelihood LIK results with start>1 (i.e. presampling>0):

the calculation speed-up construct which relies on converged covariance
matrix

lik(t) = lik(t) + reste*log(dF);

adds reste * log(dF) to the last-1 (i.e. the smpl) member of lik
(the last, the lik(smpl+1) one contains smpl*pp*log(2*pi))
but reste is usually larger than T-start+1 so that

LIK = .5*(sum(lik(start:end))-(start-1)*lik(smpl+1)/smpl)

has much more log(dF)s added than required since they are all concentrated
in the last-1 (the T) member

For example, if I change the above construct to
lik(t) = lik(t) + min(reste,(smpl-start+1))*log(dF);

the reported likelihood for presample=40 from Matlab KF is
1640935.5855267849
which is nearly the same as that from C++ KF below:
1640935.5854489324

Shall I make changes to kalman/likelihood/ KFs and upload the .m files?
This problem affects also the older versions of DiffuseLikelihood**.m too.

Best regards

George
artilogica@btconnect.com

----- Original Message ----- From: "Michel Juillard" <michel.juillard@ens.fr>
To: "G. Perendia" <george@perendia.orangehome.co.uk>
Sent: Tuesday, May 26, 2009 10:32 AM
Subject: Re: Kalman Filter+PS

Hi George,

Re 1) below:
I modified C++ KF so that it reports log-likelihood for given
start/preampling in same/similar manner as the Matlab KFs do and I am
getting approximately close results, e.g.

ll= -1640935.5854489324 for C++ and
(-) 1640482.4179242959 for Matlab KF (for start=41, i.e.

presample=40).

whilst they appear same for presample=0 (e.g.2.5906e+006), i.e.
-2590556.989730841 vs
2590556.989778722

Are those results acceptably close or should I investigate further where

the

above difference may come form?

This indicates a problem . The difference should be the same with and
without presample. It may come from the computation of the likelihood
constant. This is done in a very obscure manner in Dynare Matlab.

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