Autocovariance Estimation in the Presence of Changepoints

TL;DR

This paper introduces a Yule-Walker based estimator for autocovariance in time series with unknown mean shifts, proving its consistency and normality under certain conditions.

Contribution

It proposes a novel autocovariance estimator that accounts for mean shifts and establishes its theoretical properties.

Findings

Estimator is consistent under $m/N ightarrow 0$

Estimator is asymptotically normal

Effective for dependent series with changepoints

Abstract

This article studies estimation of a stationary autocovariance structure in the presence of an unknown number of mean shifts. Here, a Yule-Walker moment estimator for the autoregressive parameters in a dependent time series contaminated by mean shift changepoints is proposed and studied. The estimator is based on first order differences of the series and is proven consistent and asymptotically normal when the number of changepoints $m$ and the series length $N$ satisfies $m/N \rightarrow 0$ as $N \rightarrow \infty$