Point Optimal Testing with Roots That Are Functionally Local to Unity

Anna Bykhovskaya and Peter Phillips
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Anna Bykhovskaya: Department of Economics, Yale University, https://economics.yale.edu/

No 2107, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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, 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. It is shown that against FLUR\ alternatives, conventional constant point optimal tests can have extremely low power, particularly when the departure from unity occurs early in the sample period. Simulation results are reported and some implications for empirical practice are examined.

Keywords: Functional local unit root; Local to unity; Uniform confidence interval; Unit root model (search for similar items in EconPapers)
JEL-codes: C22 C65 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2017-09
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (4)

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Journal Article: Point optimal testing with roots that are functionally local to unity (2020)
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