Do Bivariate Multifractal Models Improve Volatility Forecasting in Financial Time Series? An Application to Foreign Exchange and Stock Markets

This paper examines volatility linkages and forecasting for stock and foreign exchange (FX) markets from a novel perspective by utilizing a bivariate Markov-switching multifractal model (MSM) that accounts for possible interactions between stock and FX markets. Examining daily data from the advanced G6 and emerging BRICS nations, we compare the out-of-sample volatility forecasts from GARCH, univariate MSM and bivariate MSM models. Our findings show that the GARCH model generally offers superior volatility forecasts for short horizons, particularly for FX returns in advanced markets. Multifractal models, on the other hand, offer significant improvements for longer forecast horizons, consistently across most markets. Finally, the bivariate MF model provides superior forecasts compared to the univariate alternative in most G6 countries and more consistently for FX returns, while its benefits are limited in the case of emerging markets. Overall, our findings suggest that multifractal models can indeed improve out-of-sample volatility forecasts, particularly for longer horizons, while the bivariate specification can potentially extend the superior forecast performance to shorter horizons as well.