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A new non‐parametric cross‐spectrum estimator

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  • Evangelos E. Ioannidis

Abstract

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.

Suggested Citation

  • Evangelos E. Ioannidis, 2022. "A new non‐parametric cross‐spectrum estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 808-827, September.
    • Handle: RePEc:bla:jtsera:v:43:y:2022:i:5:p:808-827
    DOI: 10.1111/jtsa.12639
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    References listed on IDEAS

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    1. Joris Chau & Rainer von Sachs, 2021. "Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 819-832, April.
    2. Chau, Van Vinh & von Sachs, Rainer, 2017. "Positive-Definite Multivariate Spectral Estimation: A Geometric Wavelet Approach," LIDAM Discussion Papers ISBA 2017002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Ming Dai, 2004. "Multivariate spectral analysis using Cholesky decomposition," Biometrika, Biometrika Trust, vol. 91(3), pages 629-643, September.
    4. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    5. Robert T. Krafty & William O. Collinge, 2013. "Penalized multivariate Whittle likelihood for power spectrum estimation," Biometrika, Biometrika Trust, vol. 100(2), pages 447-458.
    6. T. Subba Rao & M. M. Gabr, 1989. "The Estimation Of Spectrum, Inverse Spectrum And Inverse Autocovariances Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(2), pages 183-202, March.
    7. Rainer Dahlhaus, 1983. "Spectral Analysis With Tapered Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 163-175, May.
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