Robust Standard Errors for GARCH Maximum-Likelihood Estimates

Summary

The document addresses how to estimate standard errors for GARCH parameters when fitting the model by maximum likelihood. It points to the Bollerslev–Wooldridge robust inference approach and notes that the fGarch package supports it through its quasi-maximum-likelihood option.

Under QMLE, the likelihood uses a normal distribution while robust standard errors account for departures from the assumed conditional distribution. The cited result says estimates remain consistent and asymptotically normal when the mean and volatility equations are correctly specified. The response also references econometrics texts for additional discussion. This is a brief implementation pointer rather than a derivation: it does not explain the covariance calculation, diagnose model specification, or compare software implementations.

Key ideas

• Robust standard errors can be used for inference on GARCH parameters estimated by maximum likelihood.
• The fGarch package offers Bollerslev–Wooldridge style inference through its QMLE setting.
• QMLE relies on correct mean and volatility specifications for the stated consistency and asymptotic normality result.
• The document provides references but does not derive the estimator or detail implementation steps.

Tags

# GARCH Parameters Standard Errors


# GARCH Parameters Standard Errors












How do you compute the standard errors of a GARCH model estimated with MLE ?

This paper references a method by Bollerslev-Wooldridge: [...] and computed standard errors using the robust method of Bollerslev-Wooldridge

Do you know of an implementation of this method (whatever the language)?

## Answer by Bob Jansen (score 1, accepted)

https://quant.stackexchange.com/a/43691

The `fGarch` package function `garchFit()` provides this functionality if you call it with `cond.dist = 'QMLE'`. Check out the documentation on the CRAN page.

> "QMLE" stands for Quasi-Maximum Likelihood Estimation, which assumes normal distribution and uses robust standard errors for inference. Bollerslev and Wooldridge (1992) proved that if the mean and the volatility equations are correctly specified, the QML estimates are consistent and asymptotically normally distributed...

The documentation references the following book: Econometric Theory and Methods - Russell Davidson & James G. Mackinnon (section 10.3 and 10.4) and has some more details.

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