VAR-GARCH-M

[TomDoan]

That's correct for the mean. See

http://www.estima.com/forum/viewtopic.php?f=8&t=1482

for an example of variance depending upon day of the week.

[economics2012]

Hi Tom,

I have read the example but I believe that a bivariate model is more complicated than a univariate one.

I am trying to add the dummies in the variance equation as follows:


dec vect[equation] garchmeqns(%nvar)
dec vect[vect] bvec(%nvar)
dec vect[vect] garchp(%nvar)
do i=1,%nvar
compute garchmeqns(i)=%modeleqn(basevar,i)
compute bvec(i)=%eqncoeffs(garchmeqns(i))
compute garchp(i)=||%sigma(i,i)*(1-0.20-0.60)-M-T-W-H,.20,.60||
end do i

(where c=ht(1-a-b)-M-T-W-H. )


compute %%garchh=%zeros(%nvar,%nvar)
do i=1,%nvar
compute %%garchh(i,i)=garchp(i)(1)+garchp(i)(2)+garchp(i)(3)+garchp(i)(4)+garchp(i)(5)+garchp(i)(6)*uu(time-1)(i,i)+garchp(i)(7)*hh(time-1)(i,i)
end do i
end



compute b=0.0
function %%garchinit
compute bb=||1.0,0.0|b,1.0||
gset hh 1 gstart-1 = ||garchp(1)(1)+garchp(1)(2)+garchp(1)(3)+garchp(1)(4)+garchp(1)(5)/(1-garchp(1)(6)-garchp(1)(7))|0.0,garchp(2)(1)+garchp(2)(2)+garchp(2)(3)+garchp(2)(4)+garchp(2)(5)/(1-garchp(2)(6)-garchp(2)(7))||
gset uu 1 gstart-1 = hh(t)
end


P.S. where garchp(i)(2)+garchp(i)(3)+garchp(i)(4)+garchp(i)(5) stands for the dummies M, T, W, H.


Am I on the right track?

Thanks a lot.

[TomDoan]

Your garchp(1)(2),...garchp(1)(4) are the parameters, and need to be multiplied by their dummies in the calculations of the %%garchh and gset hh.

If you follow the Baillie-Bollerslev parameterization, you would actually use seven parameters for the GARCH in each variable, with garchp(x)(1),...,garchp(x)(5) as the variances for days Monday to Friday and garchp(x)(6) and garchp(x)(7) as the two "GARCH" lag parameters. The %%garchh variances are then computed using

compute %%garchh(i,i)=(1-garchp(i)(6)-garchp(i)(7))*(garchp(i)(1)*M+garchp(i)(2)*T+garchp(i)(3)*W+garchp(i)(4)*H+garchp(i)(5)*F)+$
garchp(i)(6)*uu(time-1)(i,i)+garchp(i)(7)*hh(time-1)(i,i)

and

gset hh = 1 gstart-1 = ||garchp(1)(1)*M+...+garchp(1)(5)*F|0.0,garchp(2)(1)*M+...+garch2(5)*F||

The guess values will be

compute garchp(i)=||%sigma(i,i),...total of 5...,%sigma(i,i),.20,.60||

[economics2012]

Thanks a lot Tom, but I am having an error here, can you please help identifying it?

[TomDoan]

You can't use T for a series name since it's a reserved name (for the SET time index).

I didn't change the name in this, but because this isn't part of a SET, the dummies need "TIME" subscripts.

Code: Select all

function %%garchh time
type symm %%garchh
type integer time
*
compute %%garchh=%zeros(%nvar,%nvar)
do i=1,%nvar
   compute %%garchh(i,i)=(1-garchp(i)(6)-garchp(i)(7))*(garchp(i)(1)*M(time)+garchp(i)(2)*T(time)+garchp(i)(3)*W(time)+garchp(i)(4)*H(time)+garchp(i)(5)*F(time))+$
garchp(i)(6)*uu(time-1)(i,i)+garchp(i)(7)*hh(time-1)(i,i)
end do i
end

I had a stray = on this:

gset hh 1 gstart-1 = ||garchp(1)(1)*M+garchp(1)(2)*T+garchp(1)(3)*W+garchp(1)(4)*H+garchp(1)(5)*F|0.0,garchp(2)(1)*M+garchp(2)(2)*T+garchp(2)(3)*W+garchp(2)(4)*H+garchp(2)(5)*F||

[economics2012]

I still don't understand this one:

compute garchp(i)=||%sigma(i,i),1,1,1,1,1,%sigma(i,i),.20,.60||


Again, many thanks for all your help.

[economics2012]

Also, I don't see why you multiply by (1-garchp(i)(6)-garchp(i)(7)) below:

compute %%garchh=%zeros(%nvar,%nvar)
do i=1,%nvar
compute %%garchh(i,i)=(1-garchp(i)(6)-garchp(i)(7))*(garchp(i)(1)*M(time)+garchp(i)(2)*Tu(time)+garchp(i)(3)*W(time)+garchp(i)(4)*H(time)+garchp(i)(5)*F(time))+$
garchp(i)(6)*uu(time-1)(i,i)+garchp(i)(7)*hh(time-1)(i,i)
end do i
end

[TomDoan]

## SR10. Missing Values And/Or SMPL Options Leave No Usable Data Points

Do you think the problem is in the daily data? I have gaps for holidays. So , I am not sure whether RATS daily format accept it ????

Your VAR's aren't reporting missing values. You can't have NA gaps with a recursive calculation like the GARCH variance.

I still don't understand this one:

compute garchp(i)=||%sigma(i,i),1,1,1,1,1,%sigma(i,i),.20,.60||

That's supposed to be ||%sigma(i,i),%sigma(i,i),%sigma(i,i),%sigma(i,i),%sigma(i,i),.20,.60||

(five repetitions of %sigma(i,i), one for each day of the week)

[TomDoan]

Also, I don't see why you multiply by (1-garchp(i)(6)-garchp(i)(7)) below:

compute %%garchh=%zeros(%nvar,%nvar)
do i=1,%nvar
compute %%garchh(i,i)=(1-garchp(i)(6)-garchp(i)(7))*(garchp(i)(1)*M(time)+garchp(i)(2)*Tu(time)+garchp(i)(3)*W(time)+garchp(i)(4)*H(time)+garchp(i)(5)*F(time))+$
garchp(i)(6)*uu(time-1)(i,i)+garchp(i)(7)*hh(time-1)(i,i)
end do i
end

You have to do that if the day-of-the-week effect is parameterized in terms of unconditional variances rather than variance intercepts. See the Baillie-Bollerslev article.

[economics2012]

Thanks a lot Tom, I will give it a try.

I do have another question. When I run the GARCH (1,2) OR GARCH(2,1) with one lag in the mean equation, I got errors! Can you please explain to me why?

[TomDoan]

Thanks a lot Tom, I will give it a try.

I do have another question. When I run the GARCH (1,2) OR GARCH(2,1) with one lag in the mean equation, I got errors! Can you please explain to me why?

There's a "Code" button which will let you reformat 100 lines of program into an easier to manage and read code block. I would appreciate it if you would use it.

You need two lags for the GARCH process, but with lags=1 in the mean model, it can compute the mean model starting at period 2. Lagging back 2 in the variance equation takes it out of sample (to entry 0). You'll have to bump the start period up by one to accomodate the added GARCH equation lag. If your mean equation has more lags, it isn't defined until 3 or later, so there's room for the GARCH lags.

[economics2012]

I am sorry I didn't know about the "code" button.

I am not sure I got it right. So, do you mean that I need to start the data from 1973:2 instead of 1973:1 ?

Many thanks

[TomDoan]

The GSTART, which is what is used by the MAXIMIZE, needs to be at least 1973:3 to allow space for two lags. This is discussed on page 293 of the version 8 User's Guide.

[economics2012]

Hi Tom,

Running the code for daily data and accounting for the day of the week effect give me this result:

Code: Select all

MAXIMIZE - Estimation by BFGS
Convergence in    49 Iterations. Final criterion was  0.0000034 <=  0.0000100
Daily(5) Data From 1986:01:06 To 2009:12:31
Usable Observations                      6258
Skipped/Missing (from 6259)                 1
Function Value                    -22258.4669

   Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  B                             0.005857982  0.004410815      1.32810  0.18414668
2.  BVEC(1)(1)                   -0.017187612  0.014597341     -1.17745  0.23901671
3.  BVEC(1)(2)                    0.060123708  0.021574885      2.78675  0.00532403
4.  BVEC(1)(3)                    0.027542465  0.022599354      1.21873  0.22294747
5.  BVEC(1)(4)                    0.000000000  0.000000000      0.00000  0.00000000
6.  BVEC(2)(1)                    0.005762853  0.004441507      1.29750  0.19445938
7.  BVEC(2)(2)                    0.046190846  0.014068071      3.28338  0.00102570
8.  BVEC(2)(3)                    0.008901474  0.024577363      0.36218  0.71721617
9.  BVEC(2)(4)                    0.019904373  0.010230970      1.94550  0.05171458
10. GARCHP(1)(1)                  0.439479548  0.164816862      2.66647  0.00766520
11. GARCHP(1)(2)                 -0.075708348  0.223201709     -0.33919  0.73446471
12. GARCHP(1)(3)                  0.648279094  0.251471458      2.57794  0.00993904
13. GARCHP(1)(4)                 -0.441756737  0.235726974     -1.87402  0.06092786
14. GARCHP(1)(5)                 -0.005387029  0.168472383     -0.03198  0.97449140
15. GARCHP(1)(6)                  0.104161327  0.009531225     10.92843  0.00000000
16. GARCHP(1)(7)                  0.890580041  0.009501739     93.72811  0.00000000
17. GARCHP(2)(1)                  0.115927112  0.024203096      4.78976  0.00000167
18. GARCHP(2)(2)                 -0.030752563  0.032670752     -0.94129  0.34655766
19. GARCHP(2)(3)                  0.028886206  0.035109360      0.82275  0.41065049
20. GARCHP(2)(4)                 -0.011782383  0.034019800     -0.34634  0.72908798
21. GARCHP(2)(5)                  0.011430565  0.025440282      0.44931  0.65320828
22. GARCHP(2)(6)                  0.094695751  0.007201808     13.14889  0.00000000
23. GARCHP(2)(7)                  0.893204379  0.008040614    111.08659  0.00000000

SIC for VAR   49376.60170
SIC for GARCH-M   44700.50774

Does it mean that I have daily effect on Mondays and Wednesday?

Also,

If I want to check if I still have arch effect can I still run this code:

Code: Select all

dec vect[series] ustd(%nvar)
clear(zeros) ustd
dec series[vect] garchu
compute %%garchinit()
gset garchu gstart gend = bb*yvec(t)-%%garchmu(t)
do time=gstart,gend
   compute %pt(ustd,time,%solve(%decomp(hh(time)),garchu(time)))
end do time
@mvarchtest
# ustd

Many thanks

[TomDoan]

Does it mean that I have daily effect on Mondays and Wednesday?

Yes. That would be the interpretation.