A new non-parametric estimator of the cross-spectrum of a bivariate stationary time series is proposed, which is non-quadratic in the observations. This estimator is an extension of the Capon-estimator of the spectrum of a univariate time series. The proposed estimator is designed so as to cope with the leakage effect induced by strong peaks of the marginal spectra by utilizing adaptive windowing. We study the asymptotic bias and covariance structure of the proposed estimator and prove a central limit theorem for its distribution. We also obtain a result of independent importance for the consistency rate of the cross-covariance matrix of the two series. The performance of the estimator in comparison to more traditional ones is demonstrated in a simulation study under a model exhibiting extreme characteristics, such as strong peaks in its marginal spectra. Finally, the estimator is used to judge the fit of a VAR(p) model in a real data example.

中文翻译：

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一种新的非参数交叉谱估计器

提出了一种新的双变量平稳时间序列的交叉谱非参数估计量，该估计量在观察中是非二次的。该估计器是单变量时间序列谱的 Capon 估计器的扩展。所提出的估计器旨在通过利用自适应窗口来应对由边缘光谱的强峰值引起的泄漏效应。我们研究了所提出的估计量的渐近偏差和协方差结构，并证明了其分布的中心极限定理。我们还获得了两个系列的交叉协方差矩阵的一致性率具有独立重要性的结果。与更传统的估计器相比，估计器的性能在表现出极端特征的模型下的模拟研究中得到证明，例如边缘光谱中的强峰。最后，估计器用于判断 VAR(p ) 真实数据示例中的模型。