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A new approach to nonparametric estimation of multivariate spectral density function using basis expansion

Author

Listed:
  • Shirin Nezampour

    (Shiraz University
    Marquette University)

  • Alireza Nematollahi

    (Shiraz University)

  • Robert T. Krafty

    (Emory University)

  • Mehdi Maadooliat

    (Marquette University)

Abstract

This paper develops a nonparametric method for estimating the spectral density of multivariate stationary time series using basis expansion. A likelihood-based approach is used to fit the model through the minimization of a penalized Whittle negative log-likelihood. Then, a Newton-type algorithm is developed for the computation. In this method, we smooth the Cholesky factors of the multivariate spectral density matrix in a way that the reconstructed estimate based on the smoothed Cholesky components is consistent and positive-definite. In a simulation study, we have illustrated and compared our proposed method with other competitive approaches. Finally, we apply our approach to two real-world problems, Electroencephalogram signals analysis, $$El\ Ni\tilde{n}o$$ E l N i n ~ o Cycle.

Suggested Citation

  • Shirin Nezampour & Alireza Nematollahi & Robert T. Krafty & Mehdi Maadooliat, 2024. "A new approach to nonparametric estimation of multivariate spectral density function using basis expansion," Computational Statistics, Springer, vol. 39(7), pages 3625-3641, December.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:7:d:10.1007_s00180-023-01451-4
    DOI: 10.1007/s00180-023-01451-4
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    References listed on IDEAS

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    1. Patricio Maturana-Russel & Renate Meyer, 2021. "Bayesian spectral density estimation using P-splines with quantile-based knot placement," Computational Statistics, Springer, vol. 36(3), pages 2055-2077, September.
    2. Ori Rosen & David S. Stoffer, 2007. "Automatic estimation of multivariate spectra via smoothing splines," Biometrika, Biometrika Trust, vol. 94(2), pages 335-345.
    3. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    4. Jeremy Berkowitz & Francis X. Diebold, 1998. "Bootstrapping Multivariate Spectra," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 664-666, November.
    5. Ming Dai, 2004. "Multivariate spectral analysis using Cholesky decomposition," Biometrika, Biometrika Trust, vol. 91(3), pages 629-643, September.
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