Re: [DynareDev] Kalman Filter

You are right. I didn't think of the case where start would happen after than the filter has reached stationary state. If it is what happens in your example, then it must explain the difference between the C++ and the Matlab version of the filter.

One more reason to clarify the Matlab code.

Best

Michel

G. Perendia wrote:

1. In my experience, the filter cov. determinants dF becomes

stationary after several steps (5-10), e.g. 7 and number of periods the filter is stationary is reste=smpl-7 whilst, if start =41 (presample=40) than reste is then larger than smpl -start+1=smpl-40.

2. it is not problematic to add all the determinants at once in the

last period of the stationary filter as long as we subtract from the total sum

start-1-(smpl-reste) = 41 -1 -(smpl-smpl+7)=33 determinants, or, add only min(reste,(smpl-start+1)) Best regards

George

----- Original Message -----
*From:* Stéphane Adjemian <mailto:stephane.adjemian@gmail.com>
*To:* List for Dynare developers <mailto:dev@dynare.org>
*Cc:* G. Perendia <mailto:george@perendia.orangehome.co.uk>
*Sent:* Wednesday, May 27, 2009 11:04 AM
*Subject:* Re: [DynareDev] Kalman Filter

Hi all,

I agree, the matlab code is very unclear (even if I had fun
writting it this way ;-) and prone to errors if one uses the
vector lik (Marco is using it). I would rather prefer to add the
constants outside of the loop with a (sub)vector operation, this
should be more efficient. I will do it today or tomorrow.

Best,
Stéphane.

2009/5/27 Michel Juillard <michel.juillard@ens.fr
<mailto: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 <mailto:artilogica@btconnect.com>

        ----- Original Message ----- From: "Michel Juillard"
        <michel.juillard@ens.fr <mailto:michel.juillard@ens.fr>>
        To: "G. Perendia" <george@perendia.orangehome.co.uk
        <mailto: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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-- 
Stéphane Adjemian
CEPREMAP & Université du Maine

Tel: (33)1-43-13-62-39

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