Inference in a Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model

Donald Andrews and Ming Li
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Donald Andrews: Yale University
Ming Li: National University of Singapore

No 2389, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time- varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in some time periods, time-varying nonstationarity (i.e., unit root or local-to-unit 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-statistic at a given point T in time when the parameter exhibits unit root, local-to-unity, or stationary/stationary-like behavior at time T. These results are used to construct confidence intervals and median- unbiased interval estimators for the AR parameter at any specified point in time. The confidence intervals have correct uniform asymptotic coverage probability regardless of the time-varying stationarity/ nonstationary behavior of the observations.

Pages: 40 pages
Date: 2024-05
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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