Standardizing Residuals in a GARCH-MIDAS Model

Summary

The document describes how to calculate standardized residuals after fitting a GARCH-MIDAS volatility model. First obtain the fitted conditional variance for each observation and calculate the model residual as the observed value minus its fitted value. Divide that residual by the conditional standard deviation, the square root of the conditional variance, to express it in volatility-scaled units.

This gives a basic procedure and formula, but the source offers no worked data example, diagnostics, or comparison with alternative GARCH-MIDAS specifications. Implementation depends on extracting fitted residuals and conditional variances consistently from the chosen model and on the model’s treatment of the conditional mean. The answer is brief and does not discuss how to assess whether the resulting standardized residuals meet distributional or independence assumptions.

Key ideas

• Fit the GARCH-MIDAS model and obtain its conditional variance series.
• Calculate each residual from the observed value and the model’s fitted value.
• Divide each residual by the square root of its conditional variance to standardize it.
• The answer gives a basic calculation but no diagnostics or implementation example.

Tags

# How to compute standardized residuals in GARCH-MIDAS model?


# How to compute standardized residuals in GARCH-MIDAS model?












I'm trying to compute the standardized residuals in GARCH-MIDAS model but I think that the calculation is not similar to GARCH standard models in R. As reference I have only Engle's (2012) paper in which are the equation where the residuals appear.

Someone who knows how to do it?

## Answer by Sane (score 1)

https://quant.stackexchange.com/a/80728

To compute standardized residuals in a GARCH-MIDAS model, first fit the model to your data and extract the conditional variance ($\sigma^{2}_{t}$). Then, calculate the residuals ($e_t$) as the difference between the actual and estimated values, and standardize them using $z_t = \frac{e_{t}}{\sqrt{\sigma^{2}_{t}}}$.

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