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On Confidence Intervals for Autoregressive Roots and Predictive Regression

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Abstract

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|

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1879.

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Length: 27 pages
Date of creation: Sep 2012
Date of revision:
Publication status: Published in Econometrica (May 2014), 82(3): 1177-1195
Handle: RePEc:cwl:cwldpp:1879

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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  1. Peter C.B.Phillips & Tassos Magdalinos, 2009. "Econometric Inference in the Vicinity of Unity," Working Papers CoFie-06-2009, Sim Kee Boon Institute for Financial Economics.
  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. 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.
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Cited by:
  1. 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.

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