Before revision:  We employ a quasi-maximum likelihood estimator of the MSMD parameters based on the Whittle approximation and show that it is a computationally simple and fast alternative to the maximum likelihoodestimator, and works for general MSMD specifications .
After revision:  We employ a quasi-maximum likelihood estimator of the MSMD parameters based on the Whittle approximation and establish its strong consistency and asymptotic normality for general MSMD specifications. We show that the Whittle estimation is a computationally simple and fast alternative to the maximum likelihoodestimator, and works for general MSMD specifications .