Open Access from Scandinavian Journal of Statistics: Posterior consistency for the spectral density of non-Gaussian stationary time series

 Each week, we select a recently published Open Access article to feature. This week’s article comes from the Scandinavian Journal of Statistics and extends the posterior consistency to non-Gaussian time series.

The article’s abstract is given below, with the full article available to read here.  

Tang, Y.Kirch, C.Lee, J. E., & Meyer, R. (2023). Posterior consistency for the spectral density of non-Gaussian stationary time seriesScand J Statist1– 31

Various nonparametric approaches for Bayesian spectral density estimation of stationary time series have been suggested in the literature, mostly based on the Whittle likelihood approximation. A generalization of this approximation involving a nonparametric correction of a parametric likelihood has been proposed in the literature with a proof of posterior consistency for spectral density estimation in combination with the Bernstein–Dirichlet process prior for Gaussian time series. In this article, we will extend the posterior consistency result to non-Gaussian time series by employing a general consistency theorem for dependent data and misspecified models. As a special case, posterior consistency for the spectral density under the Whittle likelihood is also extended to non-Gaussian time series. Small sample properties of this approach are illustrated with several examples of non-Gaussian time series.

More Details