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Title: GLS estimation and confidence sets for the date of a single break in models with trends Authors:  Eric Beutner - Vrije Universiteit Amsterdam (Netherlands)
Yicong Lin - Maastricht University (Netherlands) [presenting]
Stephan Smeekes - Maastricht University (Netherlands)
Abstract: The aim is to derive the asymptotics of a generalized least squares (GLS) estimator of the structural break date in the time series models with a single break in level and/or trend and stationary errors. The asymptotic distribution theory can be readily applied for testing and inference. It is found that the GLS, ordinary least squares (OLS) and GLS quasi-differencing (GLS-QD) break date estimators are asymptotically equivalent. The common asymptotic distribution of these three estimators captures the asymmetry and bimodality often observed in finite samples, and delivers good approximations in general settings. As the GLS estimator relies on the unknown inverse autocovariance matrix, we construct feasible GLS (FGLS) estimators using a consistent estimator of the inverse matrices. Monte Carlo studies show finite sample gains of the FGLS estimators when there is a strong serial correlation. Furthermore, we propose three novel constructions of confidence sets by using the FGLS break date estimators. The confidence sets are based on either a pivotal quantity or the inversion of multiple likelihood-ratio tests. The asymptotic critical value does not depend on nuisance parameters. We find that our proposed methods have fairly accurate coverages and short lengths in various simulations. When there are persistent errors and small break sizes, one of our suggested confidence sets yields good coverage and relatively short length consistently.