Should GARCH and variants be considered when modeling Realized Volatility?

Question

If I'm attempting to model & predict Realized Volatility as defined as the sum of squared intraday returns. Does it make sense to evaluate GARCH and GARCH variants? If yes, are there special considerations given that part of the model is modelling the vol of vol?

Many of the applications of GARCH models that I have come across are fit against the returns of underlying processes (equity returns, fx returns, etc.) NOT the volatility process itself. If I am trying to develop a model to predict the RV process itself, are there better options?

Answer 1

GARCH models have conditional variance as the dependent variable. They are fit on data such as financial returns to model their volatility (conditional variance).

Realized volatility has variance as the dependent variable and is estimated on data such as returns, so the picture is pretty much the same as with GARCH.

When it comes to prediction, GARCH is quite natural for it; the dependent variable is a function of lagged variables (lagged cond. variance and lagged squared returns). So you could try a GARCH model for volatility forecasting.

Meanwhile, just calculating the realized volatility from squared intraday returns does not lend itself directly to forecasting; realized volatility is based on contemporary rather than lagged data. But you can use models such as the Heterogeneous Autoregressive model of Realized Volatility, or HAR-RV (Corsi, 2009) to forecast it.

References:

• Corsi, Fulvio. (2009). "A simple approximate long-memory model of realized volatility." Journal of Financial Econometrics 7(2): 174-196.