GLS estimation and confidence sets for the date of a single break in models with trends

Eric Beutner, Yicong Lin and Stephan Smeekes

Econometric Reviews, 2023, vol. 42, issue 2, 195-219

Abstract: We develop a Feasible Generalized Least Squares estimator of the date of a structural break in level and/or trend. The estimator is based on a consistent estimate of a T-dimensional inverse autocovariance matrix. A cubic polynomial transformation of break date estimates can be approximated by a nonstandard yet nuisance parameter free distribution asymptotically. The new limiting distribution captures the asymmetry and bimodality in finite samples and is applicable for inference with a single, known, set of critical values. We consider the confidence intervals/sets for break dates based on both Wald-type tests and by inverting multiple likelihood ratio (LR) tests. A simulation study shows that the proposed estimator increases the empirical concentration probability in a small neighborhood of the true break date and potentially reduces the mean squared errors. The LR-based confidence intervals/sets have good coverage while maintaining informative length even with highly persistent errors and small break sizes.

Date: 2023
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DOI: 10.1080/07474938.2023.2178088

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