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Non-parametric seasonal unit root tests under periodic non-stationary volatility

Author

Listed:
  • Kemal Çag̃lar Gög̃ebakan

    (Oregon Health and Science University
    Oregon Health and Science University)

  • Burak Alparslan Eroglu

    (İstanbul Bilgi University
    İstanbul Bilgi University)

Abstract

This paper presents a new non-parametric seasonal unit root testing framework that is robust to periodic non-stationary volatility in innovation variance by making an extension to the fractional seasonal variance ratio unit root tests of Eroğlu et al. (Econ Lett 167:75–80, 2018). The setup allows for both periodic heteroskedasticity structure of Burridge and Taylar (J Econ 104(1):91–117, 2001) and non-stationary volatility structure of Cavaliere and Taylor (Econ Theory 24(1):43-71, 2008). We show that the limiting null distributions of the variance ratio tests depend on nuisance parameters derived from the underlying volatility process. Monte Carlo simulations show that the standard variance ratio tests can be substantially oversized in the presence of such effects. Consequently, we propose wild bootstrap implementations of the variance ratio tests. Wild bootstrap resampling schemes are shown to deliver asymptotically pivotal inference. The simulation evidence depicts that the proposed bootstrap tests perform well in practice and essentially correct the size problems observed in the standard fractional seasonal variance ratio tests, even under extreme patterns of heteroskedasticity.

Suggested Citation

  • Kemal Çag̃lar Gög̃ebakan & Burak Alparslan Eroglu, 2022. "Non-parametric seasonal unit root tests under periodic non-stationary volatility," Computational Statistics, Springer, vol. 37(5), pages 2581-2636, November.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01211-w
    DOI: 10.1007/s00180-022-01211-w
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    References listed on IDEAS

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