Forecasting the Variability of Stock Index Returns with theMultifractal Random Walk Model for Realized Volatilities
Thomas Lux,∗Cristina Sattarhoff
December 7, 2020
We compare the predictive ability of the multifractal random walk (MRW) model forrealized volatilities, short: RV-MRW, by Duchon et al. (2012) against 6 classical volatilitymodels. We also consider two extensions of the Markov-switching multifractal (MSM) modelby Calvet and Fisher (2001) for the realized volatilities. The performance of the models isevaluated out-of-sample based on the empirical MSE and MAE as well as using the superiorpredictive ability test by Hansen (2005). Overall, our extensive empirical study for 14international stock markets indices has a clear message: the RV-MRW is throughout thebest model when using the MAE criterium. In term of MSE values the RV-MRW comesout as the most successful model for large forecast horizons 10≤h≤100 days whereasthe RV-ARFIMA provides best results in the short term. Our results are very promising ifwe consider that this is the first empirical application of the RV-MRW. Moreover, whereasRV-ARFIMA forecasts are often a time consuming task, the RV-MRW stands out due to itsfast execution and straightforward implementation.JEL Classification:C20, G12Keywords:Realized volatility, multiplicative volatility models, long memory, internationalvolatility forecasting.
