Bayesian nonparametric spectral analysis of locally stationary processes
Abstract
Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood approximation is able to depict the time-frequency evolution of the process by utilizing the moving periodogram previously introduced in the bootstrap literature. The posterior distribution is obtained by updating a bivariate extension of the Bernstein-Dirichlet process prior with the dynamic Whittle likelihood. Asymptotic properties such as sup-norm posterior consistency and L2-norm posterior contraction rates are presented. Additionally, this methodology enables model selection between stationarity and non-stationarity based on the Bayes factor. The finite-sample performance of the method is investigated in simulation studies and applications to real-life data-sets are presented.
Keywords
Cite
@article{arxiv.2303.11561,
title = {Bayesian nonparametric spectral analysis of locally stationary processes},
author = {Yifu Tang and Claudia Kirch and Jeong Eun Lee and Renate Meyer},
journal= {arXiv preprint arXiv:2303.11561},
year = {2023}
}