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A new non‐parametric cross‐spectrum estimator

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.