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A functional limit theorem for self-normalized partial sum processes in the M1 topology

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  • Krizmanić, Danijel

Abstract

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index α∈(0,2) and weak dependence conditions. The convergence takes place in the space of real-valued càdlàg functions on [0,1] with the Skorokhod M1 topology.

Suggested Citation

  • Krizmanić, Danijel, 2026. "A functional limit theorem for self-normalized partial sum processes in the M1 topology," Statistics & Probability Letters, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:stapro:v:230:y:2026:i:c:s0167715225002524
    DOI: 10.1016/j.spl.2025.110607
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    References listed on IDEAS

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    1. Peligrad, Magda & Sang, Hailin, 2012. "Asymptotic Properties Of Self-Normalized Linear Processes With Long Memory," Econometric Theory, Cambridge University Press, vol. 28(3), pages 548-569, June.
    2. Wu, Wei Biao, 2006. "Unit Root Testing For Functionals Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 22(1), pages 1-14, February.
    3. Kulik, Rafal, 2006. "Limit theorems for self-normalized linear processes," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1947-1953, December.
    4. Basrak, Bojan & Segers, Johan, 2009. "Regularly varying multivariate time series," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1055-1080, April.
    5. 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.
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    • M1 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration

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