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A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter

Author

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  • Donald W. K. Andrews

    (Cowles Foundation for Research in Economics, Yale University)

  • Patrik Guggenberger

    (Pennsylvania State University)

Abstract

This paper introduces a new confidence interval (CI) for the autoregressive parameter (AR) in an AR(1) model that allows for conditional heteroskedasticity of a general form and AR parameters that are less than or equal to unity. The CI is a modification of Mikusheva's (2007a) modification of Stock's (1991) CI that employs the least squares estimator and a heteroskedasticity-robust variance estimator. The CI is shown to have correct asymptotic size and to be asymptotically similar (in a uniform sense). It does not require any tuning parameters. No existing procedures have these properties. Monte Carlo simulations show that the CI performs well in finite samples in terms of coverage probability and average length, for innovations with and without conditional heteroskedasticity. © 2014 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Suggested Citation

  • Donald W. K. Andrews & Patrik Guggenberger, 2014. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 376-381, May.
    • Handle: RePEc:tpr:restat:v:96:y:2014:i:2:p:376-381
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    Cited by:

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    3. Plakandaras, Vasilios & Gupta, Rangan & Balcilar, Mehmet & Ji, Qiang, 2022. "Evolving United States stock market volatility: The role of conventional and unconventional monetary policies," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    4. Sochi Iwuoha & Joseph I. Onochie, 2023. "Investigating the Relationship Between Canada’s Environmental Quality and GDP-Alternative Measures: An Error Correction Approach," Advances in Management and Applied Economics, SCIENPRESS Ltd, vol. 13(2), pages 1-1.
    5. Jae H. Kim & In Choi, 2017. "Unit Roots in Economic and Financial Time Series: A Re-Evaluation at the Decision-Based Significance Levels," Econometrics, MDPI, vol. 5(3), pages 1-23, September.
    6. Phillips, Peter C.B. & Lee, Ji Hyung, 2016. "Robust econometric inference with mixed integrated and mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 192(2), pages 433-450.
    7. Ronald W. Butler & Marc S. Paolella, 2017. "Autoregressive Lag—Order Selection Using Conditional Saddlepoint Approximations," Econometrics, MDPI, vol. 5(3), pages 1-33, September.
    8. Goldman, Matt & Kaplan, David M., 2017. "Fractional order statistic approximation for nonparametric conditional quantile inference," Journal of Econometrics, Elsevier, vol. 196(2), pages 331-346.
    9. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.

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    More about this item

    Keywords

    asymptotically similar; asymptotic size; autoregressive model; conditional heteroskedasticity; con dence interval; hybrid test; subsampling test; unit root;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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