{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T18:30:22Z","timestamp":1754159422999,"version":"3.41.2"},"reference-count":58,"publisher":"The Econometric Society","issue":"3","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>This paper considers nonparametric estimation and inference in first\u2010order autoregressive (AR(1)) models with deterministically time\u2010varying parameters. A key feature of the proposed approach is to allow for time\u2010varying stationarity in some time periods, time\u2010varying nonstationarity (i.e., unit root or local\u2010to\u2010unit root behavior) in other periods, and smooth transitions between the two. The estimation of the AR parameter at any time point is based on a local least squares regression method, where the relevant initial condition is endogenous. We obtain limit distributions for the AR parameter estimator and t\u2010statistic at a given point \n            <jats:italic>\u03c4<\/jats:italic> in time when the parameter exhibits unit root, local\u2010to\u2010unity, or stationary\/stationary\u2010like behavior at time \n            <jats:italic>\u03c4<\/jats:italic>. These results are used to construct confidence intervals and median\u2010unbiased interval estimators for the AR parameter at any specified point in time. The confidence intervals have correct asymptotic coverage probabilities with the coverage holding uniformly over stationary and nonstationary behavior of the observations.\n          <\/jats:p>","DOI":"10.3982\/qe2465","type":"journal-article","created":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T08:54:29Z","timestamp":1753433669000},"page":"823-858","source":"Crossref","is-referenced-by-count":1,"title":["Inference in a stationary\/nonstationary autoregressive time\u2010varying\u2010parameter model"],"prefix":"10.3982","volume":"16","author":[{"given":"Donald W. 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