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Smoothing Local-to-Moderate Unit Root Theory

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Tassos Magdalinos (University of Nottingham, UK)
Liudas Giraitis (Queen Mary, University of London, UK)

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Abstract

A limit theory is established for autoregressive time series that smooths the transition between local and moderate deviations from unity and provides a transitional form that links conventional unit root distributions and the standard normal. Edgeworth expansions of the limit theory are given. These expansions show that the limit theory that holds for values of the autoregressive coefficient that are closer to stationarity than local (i.e., deviations of the form = 1 + (c/n), where n is the sample size and c < 0) holds up to the second order. Similar expansions around the limiting Cauchy density are provided for the mildly explosive case.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1659.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1659.

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Length: 17 pages
Date of creation: May 2008
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Handle: RePEc:cwl:cwldpp:1659

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Related research
Keywords: Edgeworth expansion; Local to unity; Moderate deviations; Unit root distribution;

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. 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. [Downloadable!] (restricted)
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  2. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(1), pages 51-60, 01. [Downloadable!] (restricted)
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