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The role of information in nonstationary regression

Marsh, Patrick

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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, as well as the power of point optimal invariant tests for a unit root. Specifically these information measures indicate fractional, rather than linear trends may minimize inferential accuracy. Such is confirmed in numerical experiment.

Journal Article Type Article
Acceptance Date Mar 6, 2019
Online Publication Date Apr 15, 2019
Publication Date Apr 15, 2019
Deposit Date Mar 15, 2019
Publicly Available Date Apr 16, 2020
Journal Statistics
Print ISSN 0233-1888
Electronic ISSN 1029-4910
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Volume 53
Issue 3
Pages 656-672
DOI https://doi.org/10.1080/02331888.2019.1605516
Keywords Information, Kullback–Leibler, unit root, non-linear trend
Public URL https://nottingham-repository.worktribe.com/output/1656093
Publisher URL https://www.tandfonline.com/doi/full/10.1080/02331888.2019.1605516
Additional Information This is an Accepted Manuscript of an article published by Taylor & Francis in Statistics on15/04/2019, available online: http://www.tandfonline.com/10.1080/02331888.2019.1605516

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