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Unit Root Testing For Functionals Of Linear Processes

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  • Wu, Wei Biao

Abstract

We consider the unit root testing problem with errors being nonlinear transforms of linear processes. When the linear processes are long-range dependent, the asymptotic distributions in the unit root testing problem are shown to be functionals of Hermite processes. Functional limit theorems for nonlinear transforms of linear processes are established. The obtained results differ sharply from the classical cases where asymptotic distributions are functionals of Brownian motions.The author thanks the referee and Professor B. Hansen for their valuable suggestions. The work is supported in part by NSF grant DMS-04478704.

Suggested Citation

  • Wu, Wei Biao, 2006. "Unit Root Testing For Functionals Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 22(1), pages 1-14, February.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:01:p:1-14_06
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    Cited by:

    1. Hailin Sang & Yongli Sang, 2017. "Memory properties of transformations of linear processes," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 79-103, April.
    2. Loosveldt, L., 2023. "Multifractional Hermite processes: Definition and first properties," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 465-500.
    3. Ting Zhang & Hwai-Chung Ho & Martin Wendler & Wei Biao Wu, 2013. "Block Sampling under Strong Dependence," Papers 1312.5807, arXiv.org.
    4. Zhang, Ting & Ho, Hwai-Chung & Wendler, Martin & Wu, Wei Biao, 2013. "Block sampling under strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2323-2339.
    5. Lee, Ji Hyung, 2019. "Martingale decomposition and approximations for nonlinearly dependent processes," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 35-42.
    6. Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 706-717, March.
    7. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    8. Paul Doukhan & Ieva Grublytė & Denys Pommeret & Laurence Reboul, 2020. "Comparing the marginal densities of two strictly stationary linear processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1419-1447, December.

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