I re-post my question from the Cross Validated section as requested by another user.

I am using the beautiful "rugarch" package and presently have an issue concerning the interpretation of two asymmetry parameters: eta11 and eta21.

As per the package documentation (https://cran.r-project.org/web/packages/rugarch/rugarch.pdf), eta11 and eta21 stand for the rotation and the shift parameters respectively of the family-GARCH nested model news impact curve (NIC).

The package vignette "Introduction to the rugarch package" says that rotations are the main source of asymmetry for big shocks while shifts are the main source of asymmetry for small shocks.

Suppose then this is the coefficient matrix of my estimated MA(1)+AVGARCH(1,1) model with GED errors.

         Estimate   Std. Error     Pr(>|t|)
mu      0.007389067 0.0003317894 0.000000e+00
ma1    -0.039530532 0.0050175914 3.330669e-15
omega   0.003378155 0.0011845764 4.347480e-03
alpha1  0.312554942 0.0486658077 1.340761e-10
beta1   0.772007322 0.0304194057 0.000000e+00
eta11  -0.480489955 0.1109057794 1.474820e-05
eta21   0.415200036 0.0645903270 1.291172e-10
shape   0.837323483 0.0760468102 0.000000e+00

I cannot post the plot of the NIC since presently I do not have at least 10-point reputation on the Quantitative Finance section.

So, my questions are:

1) What is the financial interpretation of the eta11 and eta21 asymmetry coefficients that I estimated for the above model?

2) How can I compute the impact of positive vs. negative shocks on the volatility of the above model since there appears to be some asymmetry?

I know this may sound a trivial question to you. But I am a statistical modelling rookie and sometimes I cannot find my answers but through your help. So, thank you in advance for your comments.


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