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Semiparametric Tests for the Order of Integration in the Possible Presence of Level Breaks

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  • Fabrizio Iacone
  • Morten Ørregaard Nielsen
  • A. M. Robert Taylor

Abstract

Lobato and Robinson developed semiparametric tests for the null hypothesis that a series is weakly autocorrelated, or I(0), about a constant level, against fractionally integrated alternatives. These tests have the advantage that the user is not required to specify a parametric model for any weak autocorrelation present in the series. We extend this approach in two distinct ways. First, we show that it can be generalized to allow for testing of the null hypothesis that a series is I(δ) for any δ lying in the usual stationary and invertible region of the parameter space. The second extension is the more substantive and addresses the well-known issue in the literature that long memory and level breaks can be mistaken for one another, with unmodeled level breaks rendering fractional integration tests highly unreliable. To deal with this inference problem, we extend the Lobato and Robinson approach to allow for the possibility of changes in level at unknown points in the series. We show that the resulting statistics have standard limiting null distributions, and that the tests based on these statistics attain the same asymptotic local power functions as infeasible tests based on the unobserved errors, and hence there is no loss in asymptotic local power from allowing for level breaks, even where none is present. We report results from a Monte Carlo study into the finite-sample behavior of our proposed tests, as well as several empirical examples.

Suggested Citation

  • Fabrizio Iacone & Morten Ørregaard Nielsen & A. M. Robert Taylor, 2022. "Semiparametric Tests for the Order of Integration in the Possible Presence of Level Breaks," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 880-896, April.
  • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:2:p:880-896
    DOI: 10.1080/07350015.2021.1876712
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    References listed on IDEAS

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    1. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
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    Cited by:

    1. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    2. Canepa, Alessandra, 2022. "Ination Dynamics and Time-Varying Persistence: The Importance of the Uncertainty Channel," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202211, University of Turin.
    3. Canepa, Alessandra, 2024. "Inflation dynamics and persistence: The importance of the uncertainty channel," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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