A New Approach to Nonparametric Estimation of Multivariate Spectral Density Function Using Basis Expansion

Authors

Shirin Nezampour, Marquette University
Alireza Nematollahi, Shiraz University
Robert T. Krafty, Emory University
Mehdi Maadooliat, Marquette UniversityFollow

Document Type

Article

Publication Date

2024

Publisher

Springer

Source Publication

Computational Statistics

Source ISSN

0943-4062

Original Item ID

DOI: 10.1007/s00180-023-01451-4

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 Niño Cycle.

Comments

Computational Statistics, Vol. 39 (2024): 3625-3641. DOI.

Recommended Citation

Nezampour, Shirin; Nematollahi, Alireza; Krafty, Robert T.; and Maadooliat, Mehdi, "A New Approach to Nonparametric Estimation of Multivariate Spectral Density Function Using Basis Expansion" (2024). Mathematical and Statistical Science Faculty Research and Publications. 140.
https://epublications.marquette.edu/math_fac/140