GARCH with dummy (how to read coefficients)

[Bea]

Hi,

I am performing a GARCH with three dummy variables.
To avoid the variable trap, I entered just two dummy variables in the GARCH.
My problem is that I know that I have to read the coefficients as deviation from the coefficient of the constant(the dummy ommitted), but the result is not the same if I change the dummy variable to be omitted.
I know that I can solve the problem omitting the constant (typing lreturn lreturn(-1) d_d1 d_d2 d_d3) but i receive an error message.

Could you please help me? If I cannot interpret my coefficients I cannot conclude my work!

Thanks a lot,
Bea

Thi is the Eviews output:

Coefficient Std. Error z-Statistic Prob.

C 4.49E-05 7.67E-05 0.585207 0.5584
LRETURN(-1) 0.143200 0.017672 8.103173 0.0000

Variance Equation

C 1.89E-05 4.39E-07 43.07701 0.0000
RESID(-1)^2 0.230369 0.054338 4.239565 0.0000
GARCH(-1) 0.876040 0.012980 67.49164 0.0000
D_D2 -1.89E-05 4.72E-07 -40.02030 0.0000
D_D3 -1.70E-05 8.27E-07 -20.57619 0.0000

T-DIST. DOF 2.563125 0.164284 15.60182 0.0000

R-squared 0.028141 Mean dependent var 0.000247
Adjusted R-squared 0.025365 S.D. dependent var 0.007822
S.E. of regression 0.007722 Akaike info criterion -7.449121
Sum squared resid 0.146140 Schwarz criterion -7.430227
Log likelihood 9166.694 F-statistic 10.13863
Durbin-Watson stat 1.944860 Prob(F-statistic) 0.000000

[startz]

The dummy coefficients tell you the difference from the left out group. If you have groups with effects a, b, and c and omit the first group, the constant will be a and the dummies will be b-a and c-a. If you omit the second group, the constant will be b and the dummies will be a-b and c-b.

[Bea]

Dear Startz,

thank you very much for your reply. However, I am still confused.

I'll try to explain better my problem.

I have three dummy variables: d_d2 d_d3 d_d4. When I estimate the GARCH I omit one of them.
Suppose that I omit the last one. I will have this output:

Coefficient Std. Error z-Statistic Prob.

C 4.49E-05 7.67E-05 0.585207 0.5584
LRETURN(-1) 0.143200 0.017672 8.103173 0.0000

Variance Equation

C 1.89E-05 4.39E-07 43.07701 0.0000
RESID(-1)^2 0.230369 0.054338 4.239565 0.0000
GARCH(-1) 0.876040 0.012980 67.49164 0.0000
D_D2 - 1.89E-05 4.72E-07 -40.02030 0.0000
D_D3 -1.70E-05 8.27E-07 -20.57619 0.0000

So, my coefficients should be:
d_d4= 1.89E-05
d_d2= (1.89E-05- 1.89E-05)
d_d3= (1.89E-05 -1.70E-05)

Suppose that, instead, I would like to omit dummy d2. I have the following output:

Coefficient Std. Error z-Statistic Prob.

C 4.94E-05 7.78E-05 0.635664 0.5250
LRETURN(-1) 0.144305 0.017676 8.163724 0.0000

Variance Equation

C 2.83E-08 7.94E-08 0.355703 0.7221
RESID(-1)^2 0.195123 0.044303 4.404251 0.0000
GARCH(-1) 0.883472 0.012709 69.51633 0.0000
D_D3 1.53E-06 5.85E-07 2.619131 0.0088
D_D4 1.46E-05 9.25E-06 1.573964 0.1155

So, my coefficients should be:
d_d2= 2.83E-08
d_d3= (2.83E-08 + 1.53E-06)
d_d4= (2.83E-08 + 1.46E-05)

But the results for the coefficients is different and this shoul not happen, since it is indifferent which dummy variable you decide to drop.
What I am doing wrong? :(

Thank you very much for any help!

Bea

[startz]

Do you have 4 groups or 3? You generally need the same number of coefficients (intercept plus dummies) as groups.

[Bea]

I have three dummy variables and I decide to drop one of them each time, so I always have three groups (intercept + two dummy variables).

Why I have different results? It's very important for me because of course if I have different results I have also different conclusion!

Thanks
Bea

[startz]

The number of dummies doesn't decide the number of groups, the data does.

Why are you using dummy variables? What are you expecting them to do?