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Interpreting Rotation and Shift in the f-GARCH News Impact Curve

Article Quant Q&A · Author: msmna93
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Summary

This question concerns the meaning of two asymmetry parameters in a family-GARCH model estimated with a GED error distribution. It reports the package interpretation that one parameter rotates the news impact curve and the other shifts it, with rotation contributing more to asymmetry for large shocks and shift contributing more for small shocks. The author asks how to interpret estimated values and compare volatility responses to positive and negative shocks.

The document provides model estimates and standard errors, but no news impact curve plot, derivation, or computed shock impacts. It therefore frames an interpretation problem rather than supplying a method or answer. Any financial interpretation depends on the model parameterization and the scale and size of the shocks being compared; the coefficient signs alone do not give a full quantitative comparison.

Key ideas

  • The family-GARCH news impact curve uses rotation and shift parameters to represent asymmetry.
  • The cited package guidance associates rotation more with large-shock asymmetry and shift more with small-shock asymmetry.
  • The author seeks to compare volatility responses to positive and negative shocks.
  • The document gives estimates but no plotted curve or worked impact calculation.

Tags

VolatilityStatistics
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# Rotations and Shifts in the f-GARCH News Impact Curve


# Rotations and Shifts in the f-GARCH News Impact Curve












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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