Relative forecasting performance of volatility models: Monte Carlo evidence

Abstract

A Monte Carlo (MC) experiment is conducted to study the forecasting performance of a variety of volatility models under alternative data-generating processes (DGPs). The models included in the MC study are the (Fractionally Integrated) Generalized Autoregressive Conditional Heteroskedasticity models ((FI)GARCH), the Stochastic Volatility model (SV), the Long Memory Stochastic Volatility model (LMSV) and the Markov-switching Multifractal model (MSM). The MC study enables us to compare the relative forecasting performance of the models accounting for different characterizations of the latent volatility process: specifications that incorporate short/long memory, autoregressive components, stochastic shocks, Markov-switching and multifractality. Forecasts are evaluated by means of mean squared errors (MSE), mean absolute errors (MAE) and value-at-risk (VaR) diagnostics. Furthermore, complementarities between models are explored via forecast combinations. The results show that (i) the MSM model best forecasts volatility under any other alternative characterization of the latent volatility process and (ii) forecast combinations provide systematic improvements upon most single misspecified models, but are typically inferior to the MSM model even if the latter is applied to data governed by other processes.

Keywords:

• Monte Carlo methods
• Multifractal model of asset returns
• Volatility modelling
• Value at Risk

Classification:

• C2
• C5
• C22
• C53

Acknowledgments

Financial support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We would also like to thank Laurent Calvet, Adlai Fisher, Helmut Herwartz, several participants at the 3rd International Conference on Computational and Financial Econometrics, Limassol, Cyprus, October 2009, and two anonymous referees for helpful comments and suggestions. We are also particularly grateful to Predo de Lima for providing his GAUSS code for the spectral-likelihood estimation of the long-memory stochastic volatility model. The usual disclaimer applies.

Notes

We could also have used an adaptation of the spectral likelihood estimator for the short-memory SV model of equations (7) and (8). However, since QML has been used much more frequently in the literature, and we are interested in comparing the ‘representative’ models and estimation methods, we used the latter.

We need to add here that when estimating the FIGARCH model for other data-generating processes, we often had to delete a number of cases that produced MSE and MAE statistics that increased beyond any sensible boundaries. This happens particularly when the estimated parameter of fractional differentiation was close to one. Forecasts then tend to become explosive, leading to absurd predictions beyond the one-period horizon. Similar observations have been reported by Lux and Kaizoji (2007). The necessity of such corrections ‘by hand’ is a further disadvantage that further deteriorates the record of the FIGARCH model.