Autocovariance Estimation in the Presence of Changepoints

Gallagher, Colin and Killick, Rebecca and Lund, Robert and Shi, Xueheng (2022) Autocovariance Estimation in the Presence of Changepoints. Journal of the Korean Statistical Society. (In Press)

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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 $N$ satisfy $m/N \rightarrow 0$ as $N \rightarrow \infty$.