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The Impact of Persistent Cycles on Zero Frequency Unit Root Tests

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  • Tomás del Barrio Castro
  • Paulo M.M. Rodrigues
  • A. M. Robert Taylor

Abstract

In this paper we investigate the impact of non-stationary cycles on the asymptotic and finite sample properties of standard unit root tests. Results are presented for the augmented Dickey-Fuller normalised bias and t-ratio-based tests (Dickey and Fuller, 1979, and Said and Dickey, 1984), the variance ratio unit root test of Breitung (2002) and the M class of unit-root tests introduced by Stock (1999) and Perron and Ng (1996). The limiting distributions of these statistics are derived in the presence of non-stationary cycles. We show that while the ADF statistics remain pivotal (provided the test regression is properly augmented), this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994 and Ng and Perron, 1995) used to determine the order of augmentation in the ADF regression remain valid in the presence of non-stationary cycles.

Suggested Citation

  • Tomás del Barrio Castro & Paulo M.M. Rodrigues & A. M. Robert Taylor, 2011. "The Impact of Persistent Cycles on Zero Frequency Unit Root Tests," Working Papers w201124, Banco de Portugal, Economics and Research Department.
  • Handle: RePEc:ptu:wpaper:w201124
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    References listed on IDEAS

    as
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    Cited by:

    1. António Rua, 2016. "A wavelet-based multivariate multiscale approach for forecasting," Working Papers w201612, Banco de Portugal, Economics and Research Department.
    2. repec:eee:intfor:v:33:y:2017:i:3:p:581-590 is not listed on IDEAS
    3. Tomás Del Barrio Castro & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2015. "On the Behaviour of Phillips–Perron Tests in the Presence of Persistent Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(4), pages 495-511, August.
    4. repec:gam:jecnmx:v:5:y:2017:i:2:p:17-:d:95932 is not listed on IDEAS

    More about this item

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • 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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