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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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 |
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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 |
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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. |
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BYKHOVSKAYA, Anna PHILLIPS, Peter C. B. |
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BYKHOVSKAYA, Anna PHILLIPS, Peter C. B. |
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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 |
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Point optimal testing with roots that are functionally local to unity |
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Point optimal testing with roots that are functionally local to unity |
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Point optimal testing with roots that are functionally local to unity |
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point optimal testing with roots that are functionally local to unity |
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Institutional Knowledge at Singapore Management University |
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2020 |
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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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