Tail postcoloring in long-run variance estimation of time series

TL;DR

This paper introduces tail postcoloring, a novel method for long-run variance estimation in time series that improves robustness and flexibility over traditional prewhitening techniques.

Contribution

It proposes a new tail postcoloring approach that combines parametric models with nonparametric estimators, enhancing robustness and efficiency in variance estimation.

Findings

Achieves parametric rates when models are well-specified

More robust to model misspecification than standard prewhitening

Applicable to multivariate time series and real MCMC data

Abstract

Prewhitening is a common approach to deal with strong autocorrelation. In this article, we propose a new approach called tail postcoloring, motivated by it. It uses parametric models to project, or color back, the neglected tail autocovariances in nonparametric estimators onto the final estimator. This approach bridges the non-parametric variance estimator and the parametric coloring model through a scaling factor. It automatically switches between these two arms using a bandwidth parameter, without the need to transform the entire dataset into residuals, as in the standard prewhitening approach. When the coloring model is well-specified, a parametric rate can be achieved. In finite samples, it is also more robust to misspecification of the coloring model compared to the whitening model in the standard approach. Besides, it avoids severe potential variance inflation or power reduction caused by the recoloring factor in the standard approach. We show that multiple parametric models can be used to construct a multiply robust tail postcolored estimator. It also naturally works for multivariate time series. A real-data example in Markov chain Monte Carlo output analysis is provided.