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Adaptive wild bootstrap tests for a unit root with non‐stationary volatility

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  • H. Peter Boswijk
  • Yang Zu

Abstract

Recent research has emphasized that permanent changes in the innovation variance (caused by structural shifts or an integrated volatility process) lead to size distortions in conventional unit root tests. It has been shown how these size distortions can be resolved using the wild bootstrap. In this paper, we first derive the asymptotic power envelope for the unit root testing problem when the non‐stationary volatility process is known. Next, we show that under suitable conditions, adaptation with respect to the volatility process is possible, in the sense that non‐parametric estimation of the volatility process leads to the same asymptotic power envelope. Implementation of the resulting test involves cross‐validation and the wild bootstrap. A Monte Carlo experiment shows that the asymptotic results are reflected in finite sample properties, and an empirical analysis of real exchange rates illustrates the applicability of the proposed procedures.

Suggested Citation

  • H. Peter Boswijk & Yang Zu, 2018. "Adaptive wild bootstrap tests for a unit root with non‐stationary volatility," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 87-113, June.
    • Handle: RePEc:wly:emjrnl:v:21:y:2018:i:2:p:87-113
    DOI: 10.1111/ectj.12100
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    Cited by:

    1. H. Peter Boswijk & Yang Zu, 2022. "Adaptive Testing for Cointegration With Nonstationary Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 744-755, April.
    2. Zhang, Erhua & Wu, Jilin, 2020. "Adaptive estimation of AR∞ models with time-varying variances," Economics Letters, Elsevier, vol. 197(C).
    3. Skrobotov, Anton, 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.
    4. Sam Astill & David I Harvey & Stephen J Leybourne & A M Robert Taylor & Yang Zu, 2023. "CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 21(1), pages 187-227.

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