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

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  • Donald W. K. Andrews
  • Ming Li

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 $\tau$ in time when the parameter exhibits unit root, local-to-unity, or stationary/stationary-like behavior at time $\tau$. 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 asymptotic coverage probabilities with the coverage holding uniformly over stationary and nonstationary behavior of the observations.

Suggested Citation

  • Donald W. K. Andrews & Ming Li, 2024. "Inference in a Stationary/Nonstationary Autoregressive Time-Varying-Parameter Model," Papers 2411.00358, arXiv.org.
  • Handle: RePEc:arx:papers:2411.00358
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    References listed on IDEAS

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    1. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
    2. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    3. Lieberman, Offer & Phillips, Peter C.B., 2017. "A multivariate stochastic unit root model with an application to derivative pricing," Journal of Econometrics, Elsevier, vol. 196(1), pages 99-110.
    4. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23, January.
    5. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    6. Bykhovskaya, Anna & Phillips, Peter C.B., 2020. "Point optimal testing with roots that are functionally local to unity," Journal of Econometrics, Elsevier, vol. 219(2), pages 231-259.
    7. Andrews, Donald W. K., 1991. "Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 359-377, February.
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