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.

本文考虑了基于差分序列的锥形周期图的多元分数过程的半参数估计。我们通过结合Chen（2010）开发的最大有效锥度构造多元局部Whittle估计量。所提出的估计方法允许范围广泛的潜在不稳定的长期依赖序列，该序列对于具有相同差分阶数的确定趋势的存在是不变的，而无需两步过程。我们建立了所提出的估计量的一致性和渐近正态性，它们没有间断，并且通过以适度缓慢的速率增加锥度到无穷大的阶数，证明了渐近方差与非锥局部惠特尔估计的渐近方差相同。