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Point Optimal Testing with Roots That Are Functionally Local to Unity

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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.

Suggested Citation

  • Anna Bykhovskaya & Peter C. B. Phillips, 2017. "Point Optimal Testing with Roots That Are Functionally Local to Unity," Cowles Foundation Discussion Papers 2107, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2107
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d21/d2107.pdf
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    1. Ryan Greenaway-McGrevy & Peter C.B. Phillips, 2016. "Hot property in New Zealand: Empirical evidence of housing bubbles in the metropolitan centres," New Zealand Economic Papers, Taylor & Francis Journals, vol. 50(1), pages 88-113, April.
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    Cited by:

    1. Patrick Marsh, 2019. "Properties of the power envelope for tests against both stationary and explosive alternatives: the effect of trends," Discussion Papers 19/03, University of Nottingham, Granger Centre for Time Series Econometrics.

    More about this item

    Keywords

    Functional local unit root; Local to unity; Uniform confidence interval; Unit root model;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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