IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v82y2014i3p1177-1195.html
   My bibliography  Save this article

On Confidence Intervals for Autoregressive Roots and Predictive Regression

Author

Listed:
  • Peter C. B. Phillips

Abstract

Local to unity limit theory is used in applications to construct confidence intervals (CIs) for autoregressive roots through inversion of a unit root test (Stock (1991)). Such CIs are asymptotically valid when the true model has an autoregressive root that is local to unity (ρ = 1 + c/n), but are shown here to be invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Failure at the boundary implies that these CIs have zero asymptotic coverage probability in the stationary case and vicinities of unity that are wider than O(n-super-−1/3). The inversion methods of Hansen (1999) and Mikusheva (2007) are asymptotically valid in such cases. Implications of these results for predictive regression tests are explored. When the predictive regressor is stationary, the popular Campbell and Yogo (2006) CIs for the regression coefficient have zero coverage probability asymptotically, and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds. These results have obvious cautionary implications for the use of the procedures in empirical practice.

Suggested Citation

  • Peter C. B. Phillips, 2014. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Econometrica, Econometric Society, vol. 82(3), pages 1177-1195, May.
  • Handle: RePEc:wly:emetrp:v:82:y:2014:i:3:p:1177-1195
    DOI: 10.3982/ECTA11094
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA11094
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    3. Alexandros Kostakis & Tassos Magdalinos & Michalis P. Stamatogiannis, 2015. "Robust Econometric Inference for Stock Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1506-1553.
    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. Andrew Powell & Rodrigo Mariscal & Pilar Tavella, 2018. "On the Credibility of Inflation-Targeting Regimes in Latin America," Economía Journal, The Latin American and Caribbean Economic Association - LACEA, vol. 0(Spring 20), pages 1-24, May.
    2. Lee, Ji Hyung, 2016. "Predictive quantile regression with persistent covariates: IVX-QR approach," Journal of Econometrics, Elsevier, vol. 192(1), pages 105-118.
    3. Jungjun Choi & In Choi, 2019. "Maximum likelihood estimation of autoregressive models with a near unit root and Cauchy errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1121-1142, October.
    4. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    5. Zhou, Bo, 2017. "Semiparametric inference for non-LAN models," Other publications TiSEM 0ea4fd8a-937d-4c19-8f77-f, Tilburg University, School of Economics and Management.
    6. Chevillon, Guillaume & Mavroeidis, Sophocles & Zhan, Zhaoguo, 2016. "Robust inference in structural VARs with long-run restrictions," ESSEC Working Papers WP1702, ESSEC Research Center, ESSEC Business School.
    7. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, Open Access Journal, vol. 6(1), pages 1-28, March.
    8. repec:eee:finana:v:63:y:2019:i:c:p:418-430 is not listed on IDEAS
    9. Kuang-Liang Chang & Nan-Kuang Chen & Charles Ka Yui Leung, 2016. "Losing Track of the Asset Markets: the Case of Housing and Stock," International Real Estate Review, Asian Real Estate Society, vol. 19(4), pages 435-492.
    10. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    11. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    12. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2018. "The Pricing of Tail Risk and the Equity Premium: Evidence from International Option Markets," CREATES Research Papers 2018-02, Department of Economics and Business Economics, Aarhus University.
    13. Khalaf, Lynda & Saunders, Charles J., 2017. "Monte Carlo forecast evaluation with persistent data," International Journal of Forecasting, Elsevier, vol. 33(1), pages 1-10.
    14. Phillips, Peter C.B. & Lee, Ji Hyung, 2013. "Predictive regression under various degrees of persistence and robust long-horizon regression," Journal of Econometrics, Elsevier, vol. 177(2), pages 250-264.
    15. repec:gam:jecnmx:v:5:y:2017:i:3:p:43-:d:112377 is not listed on IDEAS
    16. Rodrigo Mariscal & Andrew Powell & Pilar Tavella, 2014. "On the Credibility of Inflation Targeting Regimes in Latin America," IDB Publications (Working Papers) 86253, Inter-American Development Bank.

    More about this item

    JEL classification:

    • 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:wly:emetrp:v:82:y:2014:i:3:p:1177-1195. 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: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/essssea.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.