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Unit Root Inference For Non-Stationary Linear Processes Driven By Infinite Variance Innovations

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  • Cavaliere, Giuseppe
  • Georgiev, Iliyan
  • Taylor, A.M.Robert
Abstract
The contribution of this paper is two-fold. First, we derive the asymptotic null distribution of the familiar augmented Dickey-Fuller [ADF] statistics in the case where the shocks follow a linear process driven by infinite variance innovations. We show that these distributions are free of serial correlation nuisance parameters but depend on the tail index of the infinite variance process. These distributions are shown to coincide with the corresponding results for the case where the shocks follow a finite autoregression, provided the lag length in the ADF regression satisfies the same o(T1/3) rate condition as is required in the finite variance case. In addition, we establish the rates of consistency and (where they exist) the asymptotic distributions of the ordinary least squares sieve estimates from the ADF regression. Given the dependence of their null distributions on the unknown tail index, our second contribution is to explore sieve wild bootstrap implementations of the ADF tests. Under the assumption of symmetry, we demonstrate the asymptotic validity (bootstrap consistency) of the wild bootstrap ADF tests. This is done by establishing that (conditional on the data) the wild bootstrap ADF statistics attain the same limiting distribution as that of the original ADF statistics taken conditional on the magnitude of the innovations.

Suggested Citation

  • Cavaliere, Giuseppe & Georgiev, Iliyan & Taylor, A.M.Robert, 2018. "Unit Root Inference For Non-Stationary Linear Processes Driven By Infinite Variance Innovations," Econometric Theory, Cambridge University Press, vol. 34(2), pages 302-348, April.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:02:p:302-348_00
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    Cited by:

    1. Guili Liao & Qimeng Liu & Rongmao Zhang & Shifang Zhang, 2022. "Rank test of unit‐root hypothesis with AR‐GARCH errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 695-719, September.
    2. Fatma Ozgu Serttas, 2018. "Infinite-Variance Error Structure in Finance and Economics," International Econometric Review (IER), Econometric Research Association, vol. 10(1), pages 14-23, April.
    3. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.
    4. 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.
    5. Skrobotov, Anton, 2022. "On robust testing for trend," Economics Letters, Elsevier, vol. 212(C).
    6. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    7. Pedersen, Rasmus Søndergaard, 2017. "Robust inference in conditionally heteroskedastic autoregressions," MPRA Paper 81979, University Library of Munich, Germany.
    8. Yanglin Li, 2024. "New Unit Root Tests in the Nonlinear ESTAR Framework: The Movement and Volatility Characteristics of Crude oil and Copper Prices," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1757-1776, May.
    9. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2020. "Determining the rank of cointegration with infinite variance," Discussion Papers 20/01, University of Nottingham, Granger Centre for Time Series Econometrics.

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