The University of Southampton
University of Southampton Institutional Repository

Point optimal testing with roots that are functionally local to unity

Point optimal testing with roots that are functionally local to unity
Point optimal testing with roots that are functionally local to unity
Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from unit roots. The present paper shows how to generalize LUR asymptotics to cases where the localized departure from unity is a time varying function rather than a constant. Such a functional local unit root (FLUR) model has much greater generality and encompasses many cases of additional interest that appear in practical work, including structural break formulations that admit subperiods of unit root, local stationary and local explosive behavior within a given sample. Point optimal FLUR tests are constructed in the paper to accommodate such cases and demonstrate how the power envelope changes in situations of practical interest. Against FLUR alternatives, conventional constant point optimal tests can be asymptotically infinitely deficient in power, with poor finite sample power perfor- mance particularly when the departure from unity occurs early in the sample period. New analytic explanation for this phenomenon is provided. Simulation results are reported and some implications for empirical practice are examined
Functional local unit root, Local to unity, Uniform confidence interval, Unit root model
0304-4076
231-259
Bykhovskaya, Anna
a010627a-c30d-4b8e-ac97-7550f92646f9
Phillips, Peter
f67573a4-fc30-484c-ad74-4bbc797d7243
Bykhovskaya, Anna
a010627a-c30d-4b8e-ac97-7550f92646f9
Phillips, Peter
f67573a4-fc30-484c-ad74-4bbc797d7243

Bykhovskaya, Anna and Phillips, Peter (2020) Point optimal testing with roots that are functionally local to unity. Journal of Econometrics, 219 (2), 231-259. (doi:10.1016/j.jeconom.2020.03.003).

Record type: Article

Abstract

Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from unit roots. The present paper shows how to generalize LUR asymptotics to cases where the localized departure from unity is a time varying function rather than a constant. Such a functional local unit root (FLUR) model has much greater generality and encompasses many cases of additional interest that appear in practical work, including structural break formulations that admit subperiods of unit root, local stationary and local explosive behavior within a given sample. Point optimal FLUR tests are constructed in the paper to accommodate such cases and demonstrate how the power envelope changes in situations of practical interest. Against FLUR alternatives, conventional constant point optimal tests can be asymptotically infinitely deficient in power, with poor finite sample power perfor- mance particularly when the departure from unity occurs early in the sample period. New analytic explanation for this phenomenon is provided. Simulation results are reported and some implications for empirical practice are examined

Text
FLUR_JoE_A16 - Accepted Manuscript
Download (504kB)

More information

Accepted/In Press date: 22 May 2018
e-pub ahead of print date: 28 March 2020
Published date: December 2020
Additional Information: Funding Information: Phillips acknowledges support from the National Science Foundation (NSF) under Grant No. SES 12-58258 and from the Korean Government under NRF-2014S1A2A2027803. Publisher Copyright: © 2020 Elsevier B.V.
Keywords: Functional local unit root, Local to unity, Uniform confidence interval, Unit root model

Identifiers

Local EPrints ID: 421897
URI: http://eprints.soton.ac.uk/id/eprint/421897
ISSN: 0304-4076
PURE UUID: cb17c0d7-155d-42f1-b581-68ceb67edcc1
ORCID for Peter Phillips: ORCID iD orcid.org/0000-0003-2341-0451

Catalogue record

Date deposited: 06 Jul 2018 16:30
Last modified: 23 Jul 2022 04:01

Export record

Altmetrics

Contributors

Author: Anna Bykhovskaya
Author: Peter Phillips ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×