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

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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, \(El\ Ni\tilde{n}o\) Cycle.

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Acknowledgements

The authors express sincere gratitude to the anonymous referees for their valuable and insightful comments, which significantly contributed to the enhancement of this manuscript.

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Correspondence to Mehdi Maadooliat.

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Nezampour, S., Nematollahi, A., Krafty, R.T. et al. A new approach to nonparametric estimation of multivariate spectral density function using basis expansion. Comput Stat 39, 3625–3641 (2024). https://doi.org/10.1007/s00180-023-01451-4

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