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Toward A Unified Interval Estimation Of Autoregressions

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  • Chan, Ngai Hang
  • Li, Deyuan
  • Peng, Liang

Abstract

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its asymptotic limit is always normal without assuming stationarity of the process. Unlike the bootstrap method or the least squares procedure, the proposed empirical likelihood–based confidence interval is applicable regardless of whether the underlying autoregressive process is stationary, unit root, near-integrated, or even explosive, thereby providing a unified approach for interval estimation of an AR(1) model to encompass all situations. Finite-sample simulation studies confirm the effectiveness of the proposed method.

Suggested Citation

  • Chan, Ngai Hang & Li, Deyuan & Peng, Liang, 2012. "Toward A Unified Interval Estimation Of Autoregressions," Econometric Theory, Cambridge University Press, vol. 28(3), pages 705-717, June.
    • Handle: RePEc:cup:etheor:v:28:y:2012:i:03:p:705-717_00
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    Cited by:

    1. Fukang Zhu & Zongwu Cai & Liang Peng, 2014. "Predictive regressions for macroeconomic data," Papers 1404.7642, arXiv.org.
    2. 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.
    3. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    4. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    5. Chang, Seong Yeon, 2020. "A new test of asset return predictability with an unstable predictor," Economics Letters, Elsevier, vol. 196(C).
    6. Yang, Yaxing & Ling, Shiqing, 2017. "Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 197(2), pages 368-381.
    7. Nate Millington, 2015. "From urban scar to ‘park in the sky’: terrain vague, urban design, and the remaking of New York City’s High Line Park," Environment and Planning A, , vol. 47(11), pages 2324-2338, November.
    8. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Economics and Statistics Working Papers 18-2017, Singapore Management University, School of Economics.

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