GMM estimation of Multifractal Random Walks using an efficient algorithm for HAC covariance matrix estimation

This paper improves the estimation procedure of the Multifractal Random Walk model by means of an optimal iterated Generalized Method of Moments (GMM) estimator using an enhanced moments function. We report good estimation results within the scope of a Monte Carlo simulation study, with normally distributed estimates for the intermittency coefficient λ². This allows us to construct statistical hypothesis tests about λ². Moreover, the GMM estimator proves to be robust to variations in the parameter starting values. In a financial application we estimate the Multifractal Random Walk model from the daily values of the German DAX stock market index. Throughout our study, computing time is considerably reduced by means of an efficient algorithm for Heteroscedasticity and Autocorrelation Consistent (HAC) covariance matrix estimation. This algorithm outperforms the classical HAC estimation methods developed for GAUSS or R due to a fast Toeplitz matrix-vector multiplication procedure.