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On Confidence Intervals for Autoregressive Roots and Predictive Regression



A prominent use of local to unity limit theory in applied work is the construction of confidence intervals for autogressive roots through inversion of the ADF t statistic associated with a unit root test, as suggested in Stock (1991). Such confidence intervals are valid when the true model has an autoregressive root that is local to unity (rho = 1 + (c/n)) but are 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. Consideration of the boundary case shows that these confidence intervals are invalid for stationary autoregression where they manifest locational bias and width distortion. In particular, the coverage probability of these intervals tends to zero as c approaches -infinity, and the width of the intervals exceeds the width of intervals constructed in the usual way under stationarity. Some implications of these results for predictive regression tests are explored. It is shown that when the regressor has autoregressive coefficient |rho|

Suggested Citation

  • Peter C.B. Phillips, 2012. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Cowles Foundation Discussion Papers 1879, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1879

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    References listed on IDEAS

    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.
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    Cited by:

    1. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    2. Rodrigo Mariscal & Andrew Powell & Pilar Tavella, 2014. "On the Credibility of Inflation Targeting Regimes in Latin America," IDB Publications (Working Papers) 6604, Inter-American Development Bank.
    3. Lee, Ji Hyung, 2016. "Predictive quantile regression with persistent covariates: IVX-QR approach," Journal of Econometrics, Elsevier, vol. 192(1), pages 105-118.
    4. Zhou, Bo, 2017. "Semiparametric inference for non-LAN models," Other publications TiSEM 0ea4fd8a-937d-4c19-8f77-f, Tilburg University, School of Economics and Management.
    5. repec:eee:econom:v:200:y:2017:i:1:p:17-35 is not listed on IDEAS
    6. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 1001. "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.
    7. Chambers, MJ & Kyriacou, M, 2016. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Economics Discussion Papers 17623, University of Essex, Department of Economics.
    8. 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.
    9. Khalaf, Lynda & Saunders, Charles J., 2017. "Monte Carlo forecast evaluation with persistent data," International Journal of Forecasting, Elsevier, vol. 33(1), pages 1-10.
    10. 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.
    11. repec:gam:jecnmx:v:6:y:2018:i:1:p:11-:d:134810 is not listed on IDEAS
    12. 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.
    13. repec:gam:jecnmx:v:5:y:2017:i:3:p:43-:d:112377 is not listed on IDEAS
    14. 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


    Autoregressive root; Confidence belt; Confidence interval; Coverage probability; Local to unity; Localizing coefficient; Predictive regression; Tightness;

    JEL classification:

    • 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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