kalman filter with different initial values

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simba
Posts: 1
Joined: Sat Mar 23, 2013 6:00 am

kalman filter with different initial values

Postby simba » Sun Mar 24, 2013 11:59 am

dear EViews users
I'm still a new bee (undergraduate student) in state space modelling and i would like to extract potential gdp from real gdp using the kalman filter applying the clark (1987) model.
im using a random walk with a drift were the cyclical element of gdp follows a second order auto regressive process. my specification is as follows
@ename e1
@ename e2
@evar var(e1) = exp(c(1))
@evar var(e2) = exp(c(2))
@signal lgdp_real= sv1 + sv2
@state sv1 = sv1(-1) + sv4(-1)
@state sv4 = sv4(-1) + e1
@state sv2 = c(3)*sv2(-1) + c(4)*sv3(-1) + e2
@state sv3 = sv3(-1)
where
@ename = initialising error terms
@evar var = the variance of the error term which is expresssed as an exponential to guarantee non-negative estimates.
lgdp_real = log real GDP.
sv1 = stochastic trend component but i dropped the error term to smooth the trend.
sv4 = drift term
sv2 = stationary cyclical component. AR(2) model were c(3) and c(4) are the first and second AR term respectively.

My question is with respect to the results im getting after experimenting with different initial value obtained from ols regressions. i would like to know if the probability of the state variable is important as some time they can be unit and the warning Failure to improve Likelihood after 5 iterations is it a problem and given the two results is there a way i can used to choose between them.

Sspace: KALFILTER01
Method: Maximum likelihood (Marquardt)
Date: 03/24/13 Time: 00:03
Sample: 1986M01 2012M09
Included observations: 321
Failure to improve Likelihood after 5 iterations

Coefficient Std. Error z-Statistic Prob.

C(1) -15.32697 0.062702 -244.4417 0.0000
C(2) -13.19062 0.323759 -40.74204 0.0000
C(3) 0.614780 0.000289 2127.548 0.0000
C(4) -6.976988 0.001805 -3865.954 0.0000

Final State Root MSE z-Statistic Prob.

SV1 7.608251 706.5685 0.010768 0.9914
SV4 0.001616 0.000923 1.750656 0.0800
SV2 6.881444 706.5685 0.009739 0.9922
SV3 -0.379964 39.01168 -0.009740 0.9922

Log likelihood 1534.942 Akaike info criterion -9.538580
Parameters 4 Schwarz criterion -9.491583
Diffuse priors 4 Hannan-Quinn criter. -9.519815

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Sspace: KALMAN_FILTER03
Method: Maximum likelihood (Marquardt)
Date: 03/24/13 Time: 00:05
Sample: 1986M01 2012M09
Included observations: 321
Convergence achieved after 1 iteration

Coefficient Std. Error z-Statistic Prob.

C(1) -42.25884 0.001164 -36303.03 0.0000
C(2) -13.74436 1.93E-09 -7.10E+09 0.0000
C(3) -0.106907 4.13E-11 -2.59E+09 0.0000
C(4) -13.21654 4.72E-07 -28002818 0.0000

Final State Root MSE z-Statistic Prob.

SV1 14.45534 7.250320 1.993751 0.0462
SV4 0.002243 5.57E-08 40239.76 0.0000
SV2 -0.467727 7.250320 -0.064511 0.9486
SV3 -0.094118 999.9474 -9.41E-05 0.9999

Log likelihood -45726135 Akaike info criterion 284898.1
Parameters 4 Schwarz criterion 284898.1
Diffuse priors 4 Hannan-Quinn criter. 284898.1

thank you in advance for your advice as it will strengthen my term paper
regards
simba

maya
Posts: 3
Joined: Sun Oct 27, 2013 8:35 am

Re: kalman filter with different initial values

Postby maya » Sun Oct 27, 2013 8:43 am

hi dear simba,
it is so nice that you learned so much about kalman filter now
but unfortunately i'm new-born in this matter!! :(
could you please send me your final workfile of kalman filter to training it?
i think it is good for me to start with that.

thanks
regards


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