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Towards a Unified Asymptotic Theory for Autoregression



This paper develops an asymptotic theory for a first order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive, the local alternative is explosive; and when it is zero we have the standard unit root theory. Our asymptotic theory accommodates these alternatives and helps to unify earlier theory in which the unit root case appears as a singularity of the asymptotics. The general theory is expressed in terms of functionals of a simple diffusion process. The theory has applications to continuous time estimation and to the analysis of the asymptotic power of tests for a unit root under a sequence of local alternatives.

Suggested Citation

  • Peter C.B. Phillips, 1986. "Towards a Unified Asymptotic Theory for Autoregression," Cowles Foundation Discussion Papers 782R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1986.
  • Handle: RePEc:cwl:cwldpp:782r
    Note: CFP 685.

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    References listed on IDEAS

    1. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    Cited by:

    1. Elena Pesavento, 2007. "Residuals-based tests for the null of no-cointegration: an Analytical comparison," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 111-137, January.
    2. Elena Pesavento, 2006. "Near-optimal Unit Root Test with Stationary Covariate with Better Finite Sample Size," Emory Economics 0606, Department of Economics, Emory University (Atlanta).
    3. Hyungsik Roger Moon & Peter C. B. Phillips, 2004. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometrica, Econometric Society, vol. 72(2), pages 467-522, March.


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