(E)GARCH, R^2, Groups Estimation

[math-ew]

Hi,

I am currently working on an estimation for stock volatility with a GARCH or EGARCH-model, including one exogenous variable in the Variance Equation, Credit Default Swap Spreads. Being not really familiar with Eviews, I would like to ask you 2 questions:

(1) For GARCH and EGARCH estimation, I always get negative R^2, and I don't know why. Whats the reason for R^2 to be small and negative, even if the coefficients have great p-values? What is the right criteria for the right fitting of my model, if R^2 is not? This is the output:
---------------------------------------------------------------------------------------------------------------------------
Dependent Variable: BASF_R
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 10/02/09 Time: 22:47
Sample (adjusted): 1/02/2004 10/01/2009
Included observations: 1467 after adjustments
Convergence achieved after 15 iterations
Presample variance: backcast (parameter = 0.7)
LOG(GARCH) = C(2) + C(3)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(4)
*RESID(-1)/@SQRT(GARCH(-1)) + C(5)*LOG(GARCH(-1)) + C(6)
*BASFCDSR2

Variable Coefficient, Std. Error,z-Statistic,Prob.
C 0.000646 0.000305 2.115.882 0.0344
Variance Equation
C(2) -0.357823 0.048257 -7.414.921 0.0000
C(3) 0.178114 0.021395 8.325.110 0.0000
C(4) -0.062913 0.013454 -4.676.104 0.0000
C(5) 0.975124 0.004338 2.247.641 0.0000
C(6) 4.644.460 1.753.161 2.649.191 0.0081

R-squared -0.000347 Mean dependent var 0.000302
Adjusted R-squared -0.003770 S.D. dependent var 0.018484
S.E. of regression 0.018518 Akaike info criterion -5.681.011
Sum squared resid 0.501025 Schwarz criterion -5.659.371
Log likelihood 4.173.021 Hannan-Quinn criter. -5.672.940
Durbin-Watson stat 2.008.759
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(2) For my data, it consists of stock-returns for 18 companies and the CDS-Spreads for the same companies in the same time.
Is there any possibility to estimate all this models at one time (Perhaps group? System?)? I am not interested in correlation between this companies, but in getting 18 Ouputs for further analysing.

Thank you for all answers!
matthew

[trubador]

(1) For GARCH and EGARCH estimation, I always get negative R^2, and I don't know why. Whats the reason for R^2 to be small and negative, even if the coefficients have great p-values? What is the right criteria for the right fitting of my model, if R^2 is not? This is the output:

R-squared is only valid for mean equation, whereas GARCH models deal with variance equation. Therefore, you should not worry about its value no matter what the estimation yields. Convergence properties, significance of coefficients, correlogram of residuals and squared residuals, etc. can be used for model diagnostics.

(2) For my data, it consists of stock-returns for 18 companies and the CDS-Spreads for the same companies in the same time.
Is there any possibility to estimate all this models at one time (Perhaps group? System?)? I am not interested in correlation between this companies, but in getting 18 Ouputs for further analysing.

System estimation is for multivariate analysis and therefore should be used in the case of Multivariate-GARCH models. What you are asking is a tool that automates a repetitive task, which can be done via EViews' programming language easily. You can find plenty of examples, if you search the forum.

[math-ew]

trubador,thank you for your answer.

I thought the lower part of the estimation output consideres the variance and not the mean equation. So am I right to say, that the whole lower part ouf the estimation output is useless for GARCH-Models? Or are some informations usefull (for example the akaike information criterion for fitting?).

regards,
matthew

[trubador]

You can use information criteria to check your specification, but often you'll have to write your own procedure for more advanced diagnostics since there are many other tests developed for GARCH models. You can refer to time series textbooks for additional information on the subject.

[math-ew]

hi,

i ve got some textbooks and discovered some additional tests. Unfortunately, I did not find answers to these questions

1) The questions seems perhaps to be stupid, but can someone tell me to which equation the lowest part of the output is referring to? Is it the mean equation or the variance equation?

2) In some books, they use the Akaike or Schwarz Criterion for choosing the right Garch-Model (for example Garch(1,1) or Garch(3,3)). How can they use the criterias even if the R^2 is a wrong number. I thought that R^2 and the criterias are both referring to the (same) residuals of an OLS regression. When the regression assumptions are invalid and therefore no "real" (in terms of OLS) residuals can be calculated, why the criterias work?

Even if it seems very basic, could please someone answer?
Thanks.

[trubador]

1) The questions seems perhaps to be stupid, but can someone tell me to which equation the lowest part of the output is referring to? Is it the mean equation or the variance equation?

Variance equation.

2) In some books, they use the Akaike or Schwarz Criterion for choosing the right Garch-Model (for example Garch(1,1) or Garch(3,3)). How can they use the criterias even if the R^2 is a wrong number. I thought that R^2 and the criterias are both referring to the (same) residuals of an OLS regression. When the regression assumptions are invalid and therefore no "real" (in terms of OLS) residuals can be calculated, why the criterias work?

Calculation of information criteria is based on the average log-likelihood and the number of estimated parameters.

[math-ew]

hi,

thank you. That was a helpful information.

I would like to ask another question to the assumptions of error distribution. In the Eviews Handbook is written:
" To specify the form of the conditional distribution for your errors,...". From my understanding in GARCH you should specify the distribution of the standardized errors e_t /sigma_t and not the conditional distribution of e_t. Or am I confusing something and it is the same?

thx again

[trubador]

Yes, they refer to the same thing. The term comes from the log-likelihood specification of the model and the denominator takes a fixed value in the case of unconditional estimation of variance.

[shadow]

hey guys i have a question, i estimated an egarch model, i gave my estimation results below. i want to ask something about the variance equation. i dont know how to interpret that coefficients? what c(4) c(5) and the other coefficents stand for? which one is the assymetry term?
could you please help me?


LOG(GARCH) = C(3) + C(4)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(5)
*ABS(RESID(-2)/@SQRT(GARCH(-2))) + C(6)*ABS(RESID(-3)
/@SQRT(GARCH(-3))) + C(7)*ABS(RESID(-4)/@SQRT(GARCH(-4))) +
C(8)*RESID(-1)/@SQRT(GARCH(-1)) + C(9)*LOG(GARCH(-1))

Variable Coefficient Std. Error z-Statistic Prob.

C 76.99224 842.2852 0.091409 0.9272
AR(1) 0.999988 0.000140 7161.650 0.0000

Variance Equation

C(3) -0.143164 0.017957 -7.972405 0.0000
C(4) 0.158110 0.029806 5.304708 0.0000
C(5) -0.077406 0.035337 -2.190483 0.0285
C(6) 0.196773 0.029760 6.612035 0.0000
C(7) -0.179204 0.021551 -8.315231 0.0000
C(8) 0.039603 0.005293 7.481812 0.0000
C(9) 0.992342 0.001601 619.8096 0.0000

R-squared 0.999644 Mean dependent var 6.425654
Adjusted R-squared 0.999643 S.D. dependent var 0.595884
S.E. of regression 0.011252 Akaike info criterion -6.382604
Sum squared resid 0.378153 Schwarz criterion -6.364530
Log likelihood 9547.802 Hannan-Quinn criter. -6.376101
Durbin-Watson stat 1.936290

Inverted AR Roots 1.00

[acdoker]

hi guys

do you have any reference for this explanation coz i need to use this for my research.

"R-squared is only valid for mean equation, whereas GARCH models deal with variance equation. Therefore, you should not worry about its value no matter what the estimation yields. Convergence properties, significance of coefficients, correlogram of residuals and squared residuals, etc. can be used for model diagnostics."


Thanks a lot

CANSIN