Questions on EGARCH and IGARCH

[tpr3396]

Hi guys,
Could someone please help me with this? Thanks
Q1. This is what I got from IGARCH(1,1). Could you please tell me what I should do with this?

Dependent Variable: R_JPY
Method: ML - ARCH (Marquardt) - Student's t distribution
Sample (adjusted): 1/06/1999 1/05/2009
Included observations: 2511 after adjustments
Failure to improve Likelihood after 1 iteration
Unable to evaluate derivatives at current parameter values
Presample variance: backcast (parameter = 0.7)
GARCH = C(2)*RESID(-1)^2 + (1 - C(2))*GARCH(-1)

Variable Coefficient Std. Error z-Statistic Prob.

C -0.004247 NA NA NA

Variance Equation

RESID(-1)^2 1.225047 NA NA NA
GARCH(-1) -0.225047 NA NA NA

T-DIST. DOF 20.00000 NA NA NA

Mean dependent var -0.004247 S.D. dependent var 1.107039

Q2. This is EGARCH(1,1) with 1 asymmetric order. Does C(4) mean that there is no asymmetric effect in the series because the probability is large? Thanks
Dependent Variable: R_AUD
Method: ML - ARCH (Marquardt) - Student's t distribution
Sample (adjusted): 1/06/1999 1/05/2009
Included observations: 2511 after adjustments
Convergence achieved after 11 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))

Variable Coefficient Std. Error z-Statistic Prob.

C 0.001571 0.008254 0.190328 0.8491

Variance Equation

C(2) -0.118823 0.023749 -5.003375 0.0000
C(3) 0.121916 0.020764 5.871557 0.0000
C(4) 0.009624 0.010597 0.908150 0.3638
C(5) 0.982936 0.007291 134.8214 0.0000

T-DIST. DOF 6.788451 0.985961 6.885110 0.0000

R-squared -0.000050 Mean dependent var -0.001853
Adjusted R-squared -0.000050 S.D. dependent var 0.485064
S.E. of regression 0.485076 Akaike info criterion 1.228690
Sum squared resid 590.5993 Schwarz criterion 1.242617
Log likelihood -1536.621 Hannan-Quinn criter. 1.233745
Durbin-Watson stat 2.030252

[trubador]

Q1. This is what I got from IGARCH(1,1). Could you please tell me what I should do with this?

Try one or more of the following to see if that works:
1) Change (extend/contract) your sample period.
2) Do not backcast for the presample variance (see Equation/Estimate/Options).
3) Try different starting values (see Equation/Estimate/Options).
4) Change the error distribution.

Q2. This is EGARCH(1,1) with 1 asymmetric order. Does C(4) mean that there is no asymmetric effect in the series because the probability is large?

Yes, that is correct. You cannot reject null hypothesis of no asymmetric effect with sufficient confidence, since the value of c(4) is not statistically different from zero even at %35 alpha level...

[tpr3396]

Thanks Trubador.

[tpr3396]

Hi Trubador,
For question 1, it works when I change error distribution as Normal Distribution. Could you please explain why this is happened? Thanks

[trubador]

It is difficult to tell without looking into details of your work and data. Specification of the log-likelihood function differs with respect to your choice of error distribution and the solution can get more complicated from the numerical point of view. IGARCH has an additional constraint, which may be too restrictive for the optimization process of the model. On the other hand, it may simply because the errors do not have fat tails.