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...

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Main Authors: BYKHOVSKAYA, Anna, PHILLIPS, Peter C. B.
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Language:English
Published: Institutional Knowledge at Singapore Management University 2020
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Online Access:https://ink.library.smu.edu.sg/soe_research/2367
https://ink.library.smu.edu.sg/context/soe_research/article/3366/viewcontent/SSRN_id3036507.pdf
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spelling sg-smu-ink.soe_research-33662021-01-26T01:13:17Z Point optimal testing with roots that are functionally local to unity BYKHOVSKAYA, Anna PHILLIPS, Peter C. B. 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 performance 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. 2020-12-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2367 info:doi/10.1016/j.jeconom.2020.03.003 https://ink.library.smu.edu.sg/context/soe_research/article/3366/viewcontent/SSRN_id3036507.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Functional local unit root Local to unity Uniform confidence interval Unit root model Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Functional local unit root
Local to unity
Uniform confidence interval
Unit root model
Econometrics
spellingShingle Functional local unit root
Local to unity
Uniform confidence interval
Unit root model
Econometrics
BYKHOVSKAYA, Anna
PHILLIPS, Peter C. B.
Point optimal testing with roots that are functionally local to unity
description 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 performance 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.
format text
author BYKHOVSKAYA, Anna
PHILLIPS, Peter C. B.
author_facet BYKHOVSKAYA, Anna
PHILLIPS, Peter C. B.
author_sort BYKHOVSKAYA, Anna
title Point optimal testing with roots that are functionally local to unity
title_short Point optimal testing with roots that are functionally local to unity
title_full Point optimal testing with roots that are functionally local to unity
title_fullStr Point optimal testing with roots that are functionally local to unity
title_full_unstemmed Point optimal testing with roots that are functionally local to unity
title_sort point optimal testing with roots that are functionally local to unity
publisher Institutional Knowledge at Singapore Management University
publishDate 2020
url https://ink.library.smu.edu.sg/soe_research/2367
https://ink.library.smu.edu.sg/context/soe_research/article/3366/viewcontent/SSRN_id3036507.pdf
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