Dear Jack,
I want first to thank you for detailed answer on the restriction of
the GARCH parameters.
I will look to dig some more details out if I can.
In this post I'll be as detailed as I can be. In attachment you will
find
time series used to reproduce numbers mentioned below. I'm wondering
why is there discrepancy in std errors between GIG on one side and
Eviews
on the other. I.e. to be precise difference between Sandwich
(default) and OPG or
Hessian as VCV method. As you will see I get similar results for
Eviews and GIG
for all cases except for default Sandwich estimator.
I generated returns (differences of logarithms) from this series and
the
compared what I got in Eviews to GIG with default VCV method. The
point is
that std errors do compare in GIG with Hessian or OPG and Eviews
(friend estimated this since
I do not have one. Eviews version is 7.1) but not with default. I'm
citing Gretl as tool used to estimate
parameters in my paper and now I have problem that parameters that
are significant
in with GIG (OPG) and Eviews are not so significant any more in GIG
(Sandwich).
WIG is just one example.
Can you shed some light on that ?
I would expect that all three versions are comparable. So here are
the numbers:
GIG, VCV method: Sandwich
-----------------------------------------------------------------------------------------------
Model: GJR(1,1) [Glosten et al.] (Normal)*
Dependent variable: rr1
Sample: 1999/01/01-2009/07/10 (T = 2746), VCV method: Robust
Conditional variance equation
coefficient std. error z p-value
--------------------------------------------------------
omega 2.42038e-06 1.19365e-06 2.028 0.0426 **
alpha 0.0557507 0.0114864 4.854 1.21e-06 ***
gamma 0.126791 0.0564448 2.246 0.0247 **
beta 0.931879 0.0164785 56.55 0.0000 ***
Llik: 7972.13621 AIC: -15936.27243
BIC: -15912.60082 HQC: -15927.71942
(alt. parametrization)
coefficient std. error z p-value
--------------------------------------------------------
delta 2.42038e-06 1.19365e-06 2.028 0.0426 **
alpha 0.0425096 0.00967673 4.393 1.12e-05 ***
gamma 0.0282747 0.0145806 1.939 0.0525 *
beta 0.931879 0.0164785 56.55 0.0000 ***
GIG, VCV method: OPG
-----------------------------------------------------------------------------------------------
Model: GJR(1,1) [Glosten et al.] (Normal)*
Dependent variable: ld_WIG
Sample: 1999/01/01-2009/07/10 (T = 2746), VCV method: OPG
Conditional variance equation
coefficient std. error z p-value
----------------------------------------------------------
omega 2.42038e-06 4.31481e-07 5.609 2.03e-08 ***
alpha 0.0557507 0.00529405 10.53 6.23e-026 ***
gamma 0.126791 0.0361987 3.503 0.0005 ***
beta 0.931879 0.00544076 171.3 0.0000 ***
Llik: 7972.13621 AIC: -15936.27243
BIC: -15912.60082 HQC: -15927.71942
(alt. parametrization)
coefficient std. error z p-value
----------------------------------------------------------
delta 2.42038e-06 4.31481e-07 5.609 2.03e-08 ***
alpha 0.0425096 0.00617599 6.883 5.86e-012 ***
gamma 0.0282747 0.00761659 3.712 0.0002 ***
beta 0.931879 0.00544076 171.3 0.0000 ***
EVIEWS (both parametrizations):
------------------------------------------------------------------------------------------------
Dependent Variable: DLOG(WIG)
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 07/19/11 Time: 21:25
Sample (adjusted): 1/01/1999 7/10/2009
Included observations: 2746 after adjustments
Convergence achieved after 18 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(1) + C(2)*(ABS(RESID(-1)) - C(3)*RESID(-1)) +
C(4)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
Variance Equation
C(1) 2.76E-06 4.43E-07 6.236255 0.0000
C(2) 0.058316 0.005389 10.82082 0.0000
C(3) 0.123207 0.036352 3.389241 0.0007
C(4) 0.927083 0.005282 175.5047 0.0000
R-squared -0.000320 Mean dependent var 0.000260
Adjusted R-squared 0.000044 S.D. dependent var
0.014545
S.E. of regression 0.014545 Akaike info criterion
-5.815934
Sum squared resid 0.580945 Schwarz criterion
-5.807314
Log likelihood 7989.278 Hannan-Quinn criter.
-5.812820
Durbin-Watson stat 1.897671
Dependent Variable: DLOG(WIG)
Method: ML - ARCH
Date: 07/19/11 Time: 21:23
Sample (adjusted): 1/01/1999 7/10/2009
Included observations: 2746 after adjustments
Convergence achieved after 13 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(1) + C(2)*RESID(-1)2 +
C(3)*RESID(-1)2*(RESID(-1)<0) +
C(4)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
Variance Equation
C 2.76E-06 4.43E-07 6.233082 0.0000
RESID(-1)2 0.044740 0.006424
6.964226 0.0000
RESID(-1)2*(RESID(-1)<0)
0.028845 0.007976 3.616396 0.0003
GARCH(-1) 0.927145 0.005282 175.5278 0.0000
R-squared -0.000320 Mean dependent var 0.000260
Adjusted R-squared 0.000044 S.D. dependent var
0.014545
S.E. of regression 0.014545 Akaike info criterion
-5.815963
Sum squared resid 0.580945 Schwarz criterion
-5.807343
Log likelihood 7989.318 Hannan-Quinn criter.
-5.812849
Durbin-Watson stat 1.897671