The Restricted Likelihood Ratio Test at the Boundary in Autoregressive Series

15 Pages Posted: 8 Sep 2009

See all articles by Willa W. Chen

Willa W. Chen

Texas A&M University - Department of Statistics

Rohit Deo

Stern School of Business, New York University

Multiple version iconThere are 2 versions of this paper

Date Written: August 2009

Abstract

The restricted likelihood ratio test, RLRT, for the autoregressive coefficient in autoregressive models has recently been shown to be second order pivotal when the autoregressive coefficient is in the interior of the parameter space and so is very well approximated by the chi-square distribution. In this paper, the non-standard asymptotic distribution of the RLRT for the unit root boundary value is obtained and is found to be almost identical to that of the chi-square in the right tail. Together, the above two results imply that the chi-square distribution approximates the RLRT distribution very well even for near unit root series and transitions smoothly to the unit root distribution.

Keywords: Boundary value, confidence interval, curvature, restricted likelihood, unit root

Suggested Citation

Chen, Willa W. and Deo, Rohit, The Restricted Likelihood Ratio Test at the Boundary in Autoregressive Series (August 2009). NYU Working Paper No. 2451/28230. Available at SSRN: https://ssrn.com/abstract=1469122

Willa W. Chen (Contact Author)

Texas A&M University - Department of Statistics ( email )

155 Ireland Street
447 Blocker
College Station, TX 77843
United States

Rohit Deo

Stern School of Business, New York University ( email )

44 West Fourth Street
New York, NY 10012
United States

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