The role of information in nonstationary regression. Issue 3 (4th May 2019)

• Record Type: Journal Article
• Authors: Marsh, Patrick
• Is Part Of: Statistics. Volume 53:Issue 3(2019)
• Page Start: 656
• Page End: 672
• Publication Date: 2019-05-04
• Subjects: Information -- Kullback–Leibler -- unit root -- non-linear trend; 62B10 -- 62F12 -- 62F05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2019.1605516
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: The role of standard likelihood-based measures of information and efficiency is unclear when regressions involve nonstationary data. Typically the standardized score is not asymptotically Gaussian and the standardized Hessian has a stochastic, rather than deterministic limit. Here we consider a time series regression involving a deterministic covariate which can be evaporating, slowly evolving or nonstationary. It is shown that conditional information, or equivalently, profile Kullback–Leibler and Fisher information remain informative about both the accuracy, i.e. asymptotic variance, of profile maximum likelihood estimators, and the power of point optimal invariant tests for a unit root. Specifically, these information measures indicate fractional, rather than linear trends that may minimize inferential accuracy. Such is confirmed in a numerical experiment.