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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 ?

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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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    $\begingroup$ Good points. Also, we can observe a continuous process at discrete time points, which makes GARCH suitable for either continuous or discrete series as long as the user is satisfied with a model just for the discrete time points (GARCH has nothing to say about what happens between the discrete time points). $\endgroup$ – Richard Hardy Jan 11 '18 at 8:52

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