EGARCH Inputs: Standardized Residuals Versus Raw Errors

Summary

The question concerns which innovation should enter the response function in an EGARCH(1,1) variance equation. It distinguishes the observed error, written as conditional volatility times a unit-scale noise term, from that standardized noise term. The answer says the function should use the unit-scale variable, supporting the questioner’s reading that the EGARCH specification uses the standardized innovation.

This matters because the standardized residual separates the shock’s size from the time-varying conditional volatility. The response is only a brief correction, referring to a standard EGARCH presentation; it does not derive the model, discuss alternative parameterizations, or explain how to estimate it. Readers should therefore check the precise convention used in the specification they are applying.

Key ideas

• The model distinguishes the observed error from the unit-scale innovation that generates it.
• The answer identifies the standardized innovation as the appropriate input to the EGARCH response function.
• EGARCH notation can vary, so the convention in a particular specification should be checked.

Tags

# EGARCH formulation


# EGARCH formulation












I am a bit confused about the formulation of the EGARCH(1,1) model. First, we have the error term: $\epsilon_t=\sigma_t*\zeta_t$, where $\zeta_t$ is white noise.

Now the EGARCH(1,1) should be: $$ log(\sigma_t^2)=w+\alpha_1*log(\sigma_{(t-1)}^2)+g(\zeta_t) $$ but instead I always see $g(\epsilon_t)$. does anyone know why?

Thank you

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/18224

Just a quick fix. Looking at the wikipedia entry of EGARCH: $g(\zeta_t)$ (the unit-scale random variable) seems correct - as you say.

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