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Confidence Intervals for Autoregressive Coefficients Near One

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  • Elliott, Graham
  • STOCK, JAMES H
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    Abstract

    Often we are interested in the largest root of an autoregressive process. Available methods rely on inverting t-tests to obtain confidence intervals. However, for large autoregressive roots, t-tests do not approximate asymptotically uniformly most powerful tests and do not have optimality properties when inverted for confidence intervals. We exploit the relationship between the power of tests and accuracy of confidence intervals, and suggest methods which are asymptotically more accurate than available interval construction methods. One interval, based on inverting the P(T) or Q(T) statistic, has good asymptotic accuracy and is easy to compute.

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    File URL: http://www.escholarship.org/uc/item/6ww3p59v.pdf;origin=repeccitec
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    Bibliographic Info

    Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt6ww3p59v.

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    Date of creation: 01 Jul 2000
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    Handle: RePEc:cdl:ucsdec:qt6ww3p59v

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    Related research

    Keywords: unit root; confidence intervals; point optimal tests;

    References

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    1. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January.
    2. Donald W.K. Andrews & Hong-Yuan Chen, 1992. "Approximately Median-Unbiased Estimation of Autoregressive Models with Applications to U.S. Macroeconomic and Financial Time Series," Cowles Foundation Discussion Papers 1026, Cowles Foundation for Research in Economics, Yale University.
    3. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
    4. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
    5. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-83, August.
    6. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
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