Generalized Method of Moment estimation of multivariate multifractal models

Multifractal processes have recently been introduced as a new tool for modeling the stylized facts of financial markets and have been found to consistently provide certain gains in performance over basic volatility models for a broad range of assets and for various risk management purposes. Due to computational constraints, multivariate extensions of the baseline univariate multifractal framework are, however, still very sparse so far. In this paper, we introduce a parsimoniously designed multivariate multifractal model, and we implement its estimation via a Generalized Methods of Moments (GMM) algorithm. Monte Carlo studies show that the performance of this GMM estimator for bivariate and trivariate models is similar to GMM estimation for univariate multifractal models. An empirical application shows that the multivariate multifractal model improves upon the volatility forecasts of multivariate GARCH over medium to long forecast horizons.