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Asymptotic Theory and Unified Confidence Region for an Autoregressive Model

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  • Xiaohui Liu
  • Liang Peng

Abstract

Although some unified inferences for the coefficient in an AR(1) model have been proposed in the literature, it remains open as to how to construct a unified confidence region for the intercept and the coefficient jointly without a prior on whether the sequence is stationary or unit root or near unit root or moderate deviations from a unit root or explosive and whether the sequence has a zero or nonzero constant intercept. After deriving the joint limit of the least squares estimator for all of these cases, this article proposes a unified empirical likelihood confidence region by first splitting the data into two parts and then constructing some weighted score equations. The good finite sample performance of the proposed method is demonstrated via a simulation study. Real data applications are provided as well.

Suggested Citation

  • Xiaohui Liu & Liang Peng, 2019. "Asymptotic Theory and Unified Confidence Region for an Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(1), pages 43-65, January.
    • Handle: RePEc:bla:jtsera:v:40:y:2019:i:1:p:43-65
    DOI: 10.1111/jtsa.12418
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    Cited by:

    1. Christis Katsouris, 2023. "Unified Inference for Dynamic Quantile Predictive Regression," Papers 2309.14160, arXiv.org, revised Nov 2023.
    2. Jingjie Xiang & Gangzheng Guo & Qing Zhao, 2022. "Testing for a Moderately Explosive Process with Structural Change in Drift," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(2), pages 300-333, April.
    3. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    4. Gangzheng Guo & Yixiao Sun & Shaoping Wang, 2019. "Testing for moderate explosiveness," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 73-95.

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