Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis
Methodology
2017-01-19 v1
Abstract
The Whittle likelihood is widely used for Bayesian nonparametric estimation of the spectral density of stationary time series. However, the loss of efficiency for non-Gaussian time series can be substantial. On the other hand, parametric methods are more powerful if the model is well-specified, but may fail entirely otherwise. Therefore, we suggest a nonparametric correction of a parametric likelihood taking advantage of the efficiency of parametric models while mitigating sensitivities through a nonparametric amendment. Using a Bernstein-Dirichlet prior for the nonparametric spectral correction, we show posterior consistency and illustrate the performance of our procedure in a simulation study and with LIGO gravitational wave data.
Keywords
Cite
@article{arxiv.1701.04846,
title = {Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis},
author = {Claudia Kirch and Matthew C. Edwards and Alexander Meier and Renate Meyer},
journal= {arXiv preprint arXiv:1701.04846},
year = {2017}
}