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Limit theory for moderate deviations from a unit root

  • Phillips, Peter C.B.
  • Magdalinos, Tassos

An asymptotic theory is given for autoregressive time series with a root of the form rho_{n} = 1+c/n^{alpha}, which represents moderate deviations from unity when alpha in (0,1). The limit theory is obtained using a combination of a functional law to a diffusion on D[0,infinity) and a central limit law to a scalar normal variate. For c 0, the serial correlation coefficient is shown to have a n^{alpha}rho_{n}^{n} convergence rate and a Cauchy limit distribution without assuming Gaussian errors, so an invariance principle applies when rho_{n} > 1. This result links moderate deviation asymptotics to earlier results on the explosive autoregression proved under Gaussian errors for alpha = 0, where the convergence rate of the serial correlation coefficient is (1 + c)^{n} and no invariance principle applies.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 136 (2007)
Issue (Month): 1 (January)
Pages: 115-130

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Handle: RePEc:eee:econom:v:136:y:2007:i:1:p:115-130
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  1. Liudas Giraitis & Peter C.B. Phillips, 2004. "Uniform Limit Theory for Stationary Autoregression," Cowles Foundation Discussion Papers 1475, Cowles Foundation for Research in Economics, Yale University.
  2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  3. Peter C.B. Phillips & Tassos Magadalinos, 2005. "Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence," Cowles Foundation Discussion Papers 1517, Cowles Foundation for Research in Economics, Yale University.
  4. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
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