On Confidence Intervals for Autoregressive Roots and Predictive Regression

Peter Phillips

No 1879, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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|

Keywords: Autoregressive root; Confidence belt; Confidence interval; Coverage probability; Local to unity; Localizing coefficient; Predictive regression; Tightness (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2012-09
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published in Econometrica (May 2014), 82(3): 1177-1195

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d18/d1879.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Journal Article: On Confidence Intervals for Autoregressive Roots and Predictive Regression (2014)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1879

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().