Realized Volatility Measures Volatility; Models Such as GARCH Forecast It

Summary

The document distinguishes GARCH forecasts from realized volatility (RV) measures. GARCH models use discrete observations, commonly squared returns, to estimate conditional variance and forecast volatility. RV instead aggregates high-frequency observations to form a proxy for volatility over a past interval; it is a measurement, not by itself a forecasting model. The two therefore serve different roles and cannot be compared as competing forecasts without a model that turns RV data into predictions.

Because the underlying continuous volatility process is unobservable, RV is often used as a proxy when assessing GARCH forecasts, and implied volatility may also be considered. The response notes that RV aims to be closer to the latent volatility than squared returns, while high-frequency measurement can be affected by jumps and noise. It mentions HAR-RV and Realized GARCH as examples of forecasting approaches that incorporate realized volatility. The discussion is conceptual and does not provide simulation results or establish that one approach always outperforms another.

Key ideas

• GARCH models estimate conditional variance from discrete return observations and can generate forecasts.
• Realized volatility uses high-frequency observations to measure past volatility as a proxy for an unobservable quantity.
• Realized volatility alone is not a forecasting model, so it is not a direct forecast competitor to GARCH.
• Realized volatility can help evaluate GARCH forecasts, though measurement may be affected by jumps and noise.
• HAR-RV and Realized GARCH are examples of models that use realized volatility data.

Tags

# Criticise GARCH relative to Realized Volatility


# Criticise GARCH relative to Realized Volatility












I would like to have your opinion about a simple question.

While GARCH would be useful to calculate the conditional volatility, and the RV being in some sense the "historical" volatility, what would be the shortcomings of GARCH relative to the RV in the case of predictions? (fake data simulations for instance). Is GARCH always outperformed ?

## Answer by Malick (score 3)

https://quant.stackexchange.com/a/37559

Volatility is an unobservable continuous variable defined over a period of time (formally defined as a stochastic process over an interval) whereas Garch models deal with discrete time observations to model and predict the volatility - approximated by the conditional variance (and generally uses squared returns as a measure of past volatility).

Realized Volatility is more like a volatility proxy : it doesn't model volatility but just try to measure it by using the highest frequency available without suffering of the related issue (jumps,noise..). It doesn't produce predictions.

Usually we use Realized Volatility measures to evaluate the "correctness" of Garch predictions (as we can't observe the "true" unobserved volatility - but we know that RV is closer to the true volatility than squared returns). Sometimes we also use implied volatility.

You can't compare Garch predictions to "RV predictions" because RV does not produce predictions. You need a model.

PS: Some models are based on RV measures (see HAR-RV model, Realized GARCH model...).

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