How to determine if an estimated GARCHmodel is wellspecified

[T27667]

How do I determine if my estimated GARCH(1,1) model is well specified?

Output:

Dependent variable : 100timesLogReturn
Mean Equation : ARMA (0, 0) model.
No regressor in the conditional mean
Variance Equation : GARCH (1, 1) model.
No regressor in the conditional variance
Normal distribution.

Strong convergence using numerical derivatives
Log-likelihood = -2008.98
Please wait : Computing the Std Errors ...

Robust Standard Errors (Sandwich formula)
Coefficient Std.Error t-value t-prob
Cst(V) 0.010869 0.0047526 2.287 0.0223
ARCH(Alpha1) 0.107741 0.019644 5.485 0.0000
GARCH(Beta1) 0.886280 0.019819 44.72 0.0000

No. Observations : 1516 No. Parameters : 3
Mean (Y) : 0.00664 Variance (Y) : 1.60670
Skewness (Y) : -0.07797 Kurtosis (Y) : 14.15044
Log Likelihood : -2008.982 Alpha[1]+Beta[1]: 0.99402

The sample mean of squared residuals was used to start recursion.
The positivity constraint for the GARCH (1,1) is observed.
This constraint is alpha[L]/[1 - beta(L)] >= 0.
The unconditional variance is 1.81809
The conditions are alpha[0] > 0, alpha[L] + beta[L] < 1 and alpha + beta >= 0.
=> See Doornik & Ooms (2001) for more details.
The condition for existence of the fourth moment of the GARCH is not observed.
The constraint equals 1.0113 and should be < 1.
=> See Ling & McAleer (2001) for details.

TESTS :
=======

Series #1/1: Standardized Residuals
---------
Normality Test

Statistic t-Test P-Value
Skewness -0.34030 5.4145 6.1445e-008
Excess Kurtosis 0.83624 6.6571 2.7920e-011
Jarque-Bera 73.431 .NaN 1.1339e-016
---------------
ARCH 1-2 test: F(2,1511) = 0.83706 [0.4332]
ARCH 1-5 test: F(5,1505) = 1.5701 [0.1654]
ARCH 1-10 test: F(10,1495)= 0.89224 [0.5397]

If I have understood correctly Alpha[1]+Beta[1] = 0.99402 (=~ 1) indicates that the model is misspecified, right?
On the other hand, there is no ARCH effects in the residuals as requested.
However, these residuals are not normal as assumed.

All this put together, can anybody tell me if the GARCH(1,1) model is well specified?

The data is attached btw.

[ophadnavis]

Hi,

Why are you taking 100 times logreturn as dependent variable. Can we not taken only logreturn for computation?

Regards
ophadnavis

How do I determine if my estimated GARCH(1,1) model is well specified?

Output:

Dependent variable : 100timesLogReturn
Mean Equation : ARMA (0, 0) model.
No regressor in the conditional mean
Variance Equation : GARCH (1, 1) model.
No regressor in the conditional variance
Normal distribution.

Strong convergence using numerical derivatives
Log-likelihood = -2008.98
Please wait : Computing the Std Errors ...

Robust Standard Errors (Sandwich formula)
Coefficient Std.Error t-value t-prob
Cst(V) 0.010869 0.0047526 2.287 0.0223
ARCH(Alpha1) 0.107741 0.019644 5.485 0.0000
GARCH(Beta1) 0.886280 0.019819 44.72 0.0000

No. Observations : 1516 No. Parameters : 3
Mean (Y) : 0.00664 Variance (Y) : 1.60670
Skewness (Y) : -0.07797 Kurtosis (Y) : 14.15044
Log Likelihood : -2008.982 Alpha[1]+Beta[1]: 0.99402

The sample mean of squared residuals was used to start recursion.
The positivity constraint for the GARCH (1,1) is observed.
This constraint is alpha[L]/[1 - beta(L)] >= 0.
The unconditional variance is 1.81809
The conditions are alpha[0] > 0, alpha[L] + beta[L] < 1 and alpha + beta >= 0.
=> See Doornik & Ooms (2001) for more details.
The condition for existence of the fourth moment of the GARCH is not observed.
The constraint equals 1.0113 and should be < 1.
=> See Ling & McAleer (2001) for details.

TESTS :
=======

Series #1/1: Standardized Residuals
---------
Normality Test

Statistic t-Test P-Value
Skewness -0.34030 5.4145 6.1445e-008
Excess Kurtosis 0.83624 6.6571 2.7920e-011
Jarque-Bera 73.431 .NaN 1.1339e-016
---------------
ARCH 1-2 test: F(2,1511) = 0.83706 [0.4332]
ARCH 1-5 test: F(5,1505) = 1.5701 [0.1654]
ARCH 1-10 test: F(10,1495)= 0.89224 [0.5397]

If I have understood correctly Alpha[1]+Beta[1] = 0.99402 (=~ 1) indicates that the model is misspecified, right?
On the other hand, there is no ARCH effects in the residuals as requested.
However, these residuals are not normal as assumed.

All this put together, can anybody tell me if the GARCH(1,1) model is well specified?

The data is attached btw.

[T27667]

I just multiplied by 100 in order to avoid small numbers in the series, but you can do both

[ophadnavis]

How do you specify positive constraint for alpha and beta in eviews?