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

Shirin Nezampour (), Alireza Nematollahi (), Robert T. Krafty () and Mehdi Maadooliat ()
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Shirin Nezampour: Shiraz University
Alireza Nematollahi: Shiraz University
Robert T. Krafty: Emory University
Mehdi Maadooliat: Marquette University

Computational Statistics, 2024, vol. 39, issue 7, No 8, 3625-3641

Abstract: 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.

Keywords: Multivariate time series; Spectral analysis; Smoothing spline; Whittle likelihood; Regularization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01451-4

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