Aggregating Daily GARCH Variances into Monthly Volatility

Summary

The document addresses how to combine daily conditional variance estimates from a GARCH model for use with monthly observations. It identifies Drost–Nijman scaling as a literature-based method for aggregating volatility estimates from weak GARCH processes. This offers an alternative to simply converting daily volatility to a monthly scale using the square-root-of-time rule.

The answer notes that square-root scaling is commonly used under an independent and identically distributed returns assumption, but points to published discussion of its weaknesses. It also directs readers to a paper that discusses Drost–Nijman scaling. No formulas, numerical example, or recommendation tailored to a particular GARCH specification are included, so the note is best treated as a pointer to methods and assumptions that should be examined before constructing a monthly regression variable.

Key ideas

• Drost–Nijman scaling is cited for aggregating volatility estimates from weak GARCH processes.
• Square-root scaling relies on an independent and identically distributed returns assumption.
• The referenced literature discusses limitations of simple square-root scaling and the alternative method.
• The document gives no calculation or model-specific aggregation instructions.

Tags

# How to convert daily conditional variances into monthly?


# How to convert daily conditional variances into monthly?












I have a time series of daily returns and and I computed the conditional variances by means of a Garch model. Now I would like to built a regression with some other monthly data and the previously computed daily variances. What is the best way to deal with it? How would I convert the daily into monthly variances?

## Answer by NaN (score 1)

https://quant.stackexchange.com/a/31773

One of the approaches in Literature to aggregate volatility estimates from "weak" GARCH processes is the Drost Nijman scaling as presented in http://finance.martinsewell.com/stylized-facts/dependence/DrostNijman1993.pdf.

Though the square root scaling approach (based on an i.i.d. assumption for returns) is probably often used, refer the paper by Diebold for some weaknesses. http://www.ssc.upenn.edu/~fdiebold/papers/paper18/dsi.pdf. This paper also contains a discussion on the Drost Nijman volatility scaling.

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