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

Author

Listed:
  • 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:

    1. David M. Kaplan & Matt Goldman, 2015. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1503, Department of Economics, University of Missouri.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. Ronald W. Butler & Marc S. Paolella, 2017. "Autoregressive Lag—Order Selection Using Conditional Saddlepoint Approximations," Econometrics, MDPI, vol. 5(3), pages 1-33, September.
    7. 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.
    8. 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.
    9. Mohitosh Kejriwal & Xuewen Yu & Pierre Perron, 2020. "Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 676-690, September.
    10. Qing Liu & Chiyu Xia & Xiaohui Liu, 2025. "Limit theory for an AR(1) model with intercept and a possible infinite variance," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 615-630, June.

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    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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