IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1812r.html
   My bibliography  Save this paper

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

Author

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 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.

Suggested Citation

  • Donald W.K. Andrews & Patrik Guggenberger, 2011. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," Cowles Foundation Discussion Papers 1812R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2012.
  • Handle: RePEc:cwl:cwldpp:1812r
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d18/d1812-r.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    2. Romano, Joseph P & Wolf, Michael, 2001. "Subsampling Intervals in Autoregressive Models with Linear Time Trend," Econometrica, Econometric Society, vol. 69(5), pages 1283-1314, September.
    3. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    4. 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.
    5. Cribari-Neto, Francisco, 2004. "Asymptotic inference under heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 215-233, March.
    6. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    7. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October.
    8. 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.
    9. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    10. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    11. Kristensen, Dennis & Linton, Oliver, 2006. "A Closed-Form Estimator For The Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 22(2), pages 323-337, April.
    12. Ma Jun & Nelson Charles R & Startz Richard, 2007. "Spurious Inference in the GARCH (1,1) Model When It Is Weakly Identified," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(1), pages 1-27, March.
    13. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    14. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
    15. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    16. Elliott, Graham & Stock, James H., 2001. "Confidence intervals for autoregressive coefficients near one," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 155-181, July.
    17. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    18. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    19. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
    20. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Hybrid and Size-Corrected Subsample Methods," Cowles Foundation Discussion Papers 1606, Cowles Foundation for Research in Economics, Yale University.
    21. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    22. Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, May.
    23. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Matt Goldman & David M. Kaplan, 2018. "Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 136-169, June.
    3. 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.
    4. Vasilios Plakandaras & Rangan Gupta & Mehmet Balcilar & Qiang Ji, 2021. "Evolving United States Stock Market Volatility: The Role of Conventional and Unconventional Monetary Policies," Working Papers 202113, University of Pretoria, Department of Economics.
    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, Open Access Journal, 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, Open Access Journal, 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    2. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    3. 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.
    4. Claude Lopez & Christian J. Murray & David H. Papell, 2013. "Median-unbiased estimation in DF-GLS regressions and the PPP puzzle," Applied Economics, Taylor & Francis Journals, vol. 45(4), pages 455-464, February.
    5. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    6. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Hybrid and Size-Corrected Subsample Methods," Cowles Foundation Discussion Papers 1606, Cowles Foundation for Research in Economics, Yale University.
    7. Fallahi, Firouz & Voia, Marcel-Cristian, 2015. "Convergence and persistence in per capita energy use among OECD countries: Revisited using confidence intervals," Energy Economics, Elsevier, vol. 52(PA), pages 246-253.
    8. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.
    9. Rossi, Barbara, 2005. "Confidence Intervals for Half-Life Deviations From Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 432-442, October.
    10. Carlos A. Medel & Pablo M. Pincheira, 2016. "The out-of-sample performance of an exact median-unbiased estimator for the near-unity AR(1) model," Applied Economics Letters, Taylor & Francis Journals, vol. 23(2), pages 126-131, February.
    11. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
    12. Lopez, Claude & Murray, Christian J & Papell, David H, 2005. "State of the Art Unit Root Tests and Purchasing Power Parity," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(2), pages 361-369, April.
    13. Nikolay Gospodinov & Ye Tao, 2011. "Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 379-405, August.
    14. Elena Pesavento & Barbara Rossi, 2006. "Small‐sample confidence intervals for multivariate impulse response functions at long horizons," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1135-1155, December.
    15. Kim, Hyeongwoo & Durmaz, Nazif, 2012. "Bias correction and out-of-sample forecast accuracy," International Journal of Forecasting, Elsevier, vol. 28(3), pages 575-586.
    16. Fallahi, Firouz, 2012. "The stationarity of consumption–income ratios: Evidence from bootstrapping confidence intervals," Economics Letters, Elsevier, vol. 115(1), pages 137-140.
    17. Jardet, Caroline & Monfort, Alain & Pegoraro, Fulvio, 2013. "No-arbitrage Near-Cointegrated VAR(p) term structure models, term premia and GDP growth," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 389-402.
    18. Kim, Jae H. & Silvapulle, Param & Hyndman, Rob J., 2007. "Half-life estimation based on the bias-corrected bootstrap: A highest density region approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3418-3432, April.
    19. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    20. Carlos Usabiaga & Diego Romero-Ávila, 2012. "New Disaggregate Evidence on Spanish Inflation Persistence," EcoMod2012 3800, EcoMod.

    More about this item

    Keywords

    Asymptotically similar; Asymptotic size; Autoregressive model; Conditional heteroskedasticity; Confidence 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1812r. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Regan). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.