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

Author

Listed:
  • Donald W. K. Andrews

    (Yale University)

  • Ming Li

    (National University of Singapore)

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.

Suggested Citation

  • Donald W. K. Andrews & Ming Li, 2024. "Inference in a Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model," Cowles Foundation Discussion Papers 2389, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2389
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    File URL: https://cowles.yale.edu/sites/default/files/2024-05/d2389.pdf
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    References listed on IDEAS

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