On Tue, 8 Mar 2011, cociuba wrote: There's a fundamental notation problem here. Lee's book follows the notation in Hill et al, which in turn is based on what I believe EViews uses. The trouble is that what EViews calls a TGARCH is not the same thing as what gig calls a TARCH. The model described in eq. 14.9 in Lee's book corresponds to what gig calls a GJR model, with different notation. Lee's TARCH: h_t = delta + alpha_1 e_{t-1}^2 + gamma d_{t-1} e_{t-1}^2 + beta_1 h_{t-1} Gig's GJR: h_t = omega + alpha (|e_{t-1}| - gamma e_{t-1})^2 + beta h_{t-1} so the correspondence between Eviews notation and gig notation is delta = omega alpha_1 = alpha * (1-gamma)^2 gamma = 4 * alpha * gamma beta_1 = beta If you use gig to estimate a GJR model, you get: omega 0.356018 0.0723963 4.918 8.76e-07 *** alpha 0.476325 0.0760667 6.262 3.80e-10 *** gamma 0.257023 0.0705906 3.641 0.0003 *** beta 0.286992 0.0700316 4.098 4.17e-05 *** The above, in the Eviews parametrisation, would give delta 0.35602 alpha 0.26294 gamma 0.48971 beta 0.28699 which is roughly what you get in Lee's book. Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti

Just to quote Jack :) In the meantime, though, you may find it useful to have a look at Lee Adkins' online book http://www.learneconometrics.com/gretl/ebook.pdf especially chapter 14. You will find easy to use GARCH-in-mean there. Davor On 8.3.2011. 16:37, Riccardo (Jack) Lucchetti wrote:

First short question: How to get gig_estimate coefficients ? I tried as: b = gig_setup(y,3) gig_estimate(&b) matrix g4 = $coeff or g4 = $coeff[3] but I get this error code: ? matrix g4 = $coeff The statistic you requested is not available On the TARCH subject: The comparison of threshold GARCH (TGARCH) model by Zakoian (1994) defined as: sigma_t=sqrt(h_t) sigma_t = alpha_0 + (alpha_1 + gamma_1 d_{t-1}) |e_{t-1}|+ beta_1 sigma_{t-1} with delta=1 in GIG help eq(5): sigma_t = alpha'_0+ alpha'_1 (|e_{t-1}| - gamma'_1 e_{t-1}) + beta'_1 sigma_{t-1} I replicated the same procedure from GJR process (for which I got correct transformation rules) the comparison was made by transforming second eq as: alpha'_1 (|e_{t-1}| - gamma'_1 e_{t-1}) = alpha'_1 (1 - gamma'_1 sign(e_{t-1}))|e_{t-1}| the transformation rules I got are: alpha_0 = alpha'_0 alpha_1 = alpha'_1*(1-gamma'_1) gamma_1 = 2*alpha'_1*gamma'_1 beta_1 = beta'_1 then I used this script to convince myself that all is good: <script> include gig.gfn open djclose y = 100*ldiff(djclose) y -= mean(y) b2 = gig_setup(y,4) gig_estimate(&b2) scalar omega = 0.01 scalar alpha = 0.04 scalar gamma = 0.6 scalar beta = 0.8 mle ll = -0.5*(log(h^2) + (e^2)/h^2) series h = sqrt(var(y)) series e = y series ea = abs(e) series eam = ea * (e<0) series h = omega + alpha*ea(-1) + gamma*eam(-1) + beta*h(-1) params omega alpha gamma beta end mle </script> On 4.7.2011. 9:42, Riccardo (Jack) Lucchetti wrote:

Thanks a lot :) On 10.7.2011. 17:14, Riccardo (Jack) Lucchetti wrote:

Sorry for this post. I restarted Gretl and I got correct values. Something went wrong originally. On 11.7.2011. 15:08, Davor Horvatic wrote:

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

On Wed, 20 Jul 2011, Davor Horvatic wrote: I put some of that into the gig pdf doc; when CVS comes back up and you can download it, your comments are welcome. [...] Allin's script shows very clearly how things are done in gig. If you ask me if I believe that's correct, my answer is yes. If you ask me if everything else is wrong, my answer is no. As Allin said, there is a number of asymptotically equivalent ways to obtain robust vcv matrices; the trouble is, they may be very different from one another in finite samples (and yes, 2746 observations may well be "not enough"). One possible difference is, as Allin said, the type of bread you use in the sandwich: Hessian or information matrix? Another difference may come from the fact that I used the delta method to compute the vcv for the alternate parametrisation. Again, this is a quadratic form with the Jacobian acting as the "bread" and the vcv for the original parametrisation as the "ham". The choice of the type of ham should make no difference asymptotically, but in finite samples it does. Moreover, your model seems to be misspecified in at least one respect: if you run the following script fragment <hansl> foo = gig_setup(ld_WIG, 3) gig_estimate(&foo, 0) series u = foo["stduhat"] summary u normtest u --all gig_set_dist(&foo, 1) gig_estimate(&foo) </hansl> you will see that assuming conditional normality is likely to be a very bad idea; actually, if the "true" distribution is t with 5.9 degrees of freedom I'm not even sure that the conditions for asymptotic normality are satisfied (I'd need to check). In a setting such as this, I'm not at all surprised that alternative choices for robust inference may yield largely different results. Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti