A note on confidence intervals for parameter estimates of a spatio-temporal Ornstein-Uhlenbeck process

TL;DR

This paper compares two methods for constructing confidence intervals for parameters of a Gaussian spatio-temporal Ornstein-Uhlenbeck process, highlighting the advantages of a parametric bootstrap over pairwise likelihood approximations.

Contribution

It introduces a comparison between pairwise likelihood and parametric bootstrap methods for confidence interval estimation in spatio-temporal Ornstein-Uhlenbeck processes.

Findings

Bootstrap confidence intervals have better coverage than likelihood-based ones.

Likelihood-based intervals are more affected by high dimensionality.

Bootstrap method is more reliable for parameter inference in this context.

Abstract

We compare two ways of constructing confidence intervals for the moments-matching parameter estimates of a Gaussian spatio-temporal Ornstein-Uhlenbeck process. It was found that those obtained via pairwise likelihood approximations had lower coverages and were more prone to the curse of dimensionality as opposed to those from a parametric bootstrap procedure.