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Wild bootstrap seasonal unit root tests for time series with periodic nonstationary volatility

Author

Listed:
  • Giuseppe Cavaliere
  • Anton Skrobotov
  • A. M. Robert Taylor

Abstract

We investigate the behavior of the well-known Hylleberg, Engle, Granger and Yoo (HEGY) regression-based seasonal unit root tests in cases where the driving shocks can display periodic nonstationary volatility and conditional heteroskedasticity. Our set up allows for periodic heteroskedasticity, nonstationary volatility and (seasonal) generalized autoregressive-conditional heteroskedasticity as special cases. We show that the limiting null distributions of the HEGY tests depend, in general, on nuisance parameters which derive from the underlying volatility process. Monte Carlo simulations show that the standard HEGY tests can be substantially oversized in the presence of such effects. As a consequence, we propose wild bootstrap implementations of the HEGY tests. Two possible wild bootstrap resampling schemes are discussed, both of which are shown to deliver asymptotically pivotal inference under our general conditions on the shocks. Simulation evidence is presented which suggests that our proposed bootstrap tests perform well in practice, largely correcting the size problems seen with the standard HEGY tests even under extreme patterns of heteroskedasticity, yet not losing finite sample relative to the standard HEGY tests.

Suggested Citation

  • Giuseppe Cavaliere & Anton Skrobotov & A. M. Robert Taylor, 2019. "Wild bootstrap seasonal unit root tests for time series with periodic nonstationary volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 509-532, May.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:5:p:509-532
    DOI: 10.1080/07474938.2017.1348684
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    Cited by:

    1. Anton Skrobotov, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    2. Mihaela Simionescu & Wadim Strielkowski & Nicolas Schneider & Luboš Smutka, 2022. "Convergence behaviours of energy series and GDP nexus hypothesis: A non-parametric Bayesian application," PLOS ONE, Public Library of Science, vol. 17(8), pages 1-25, August.
    3. Zou, Nan & Politis, Dimitris N., 2021. "Bootstrap seasonal unit root test under periodic variation," Econometrics and Statistics, Elsevier, vol. 19(C), pages 1-21.
    4. Tom'as del Barrio Castro & Alain Hecq & Sean Telg, 2026. "Seasonality in Mixed Causal-Noncausal Processes," Papers 2604.07040, arXiv.org.
    5. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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