Efficient tapered local Whittle estimation of multivariate fractional processes

The semiparametric estimation of multivariate fractional processes based on the tapered periodogram of the differenced series is considered in this paper. We construct multivariate local Whittle estimators by incorporating the maximal efficient taper developed by Chen (2010). The proposed estimation method allows a wide range of potentially nonstationary long-range dependent series, being invariant to the presence of deterministic trends with the same extent of the differencing order, without a two-step procedure. We establish the consistency and asymptotic normality of the proposed estimators, which have no discontinuities, and show that the asymptotic variance is the same as that of the nontapered local Whittle estimation by increasing the order of a taper to infinity with a moderately slow rate. We examine the finite sample behavior of the proposed estimators through a simulation experiment.