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A note on joint functional convergence of partial sum and maxima for linear processes

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  • Krizmanić, Danijel

Abstract

Recently, for the joint partial sum and partial maxima processes constructed from linear processes with independent identically distributed innovations that are regularly varying with tail index α∈(0,2), a functional limit theorem with the Skorohod weak M2 topology has been obtained. In this paper we show that, if all the coefficients of the linear processes are of the same sign, the functional convergence holds in the stronger topology, i.e. in the Skorohod weak M1 topology on the space of R2-valued càdlàg functions on [0,1].

Suggested Citation

  • Krizmanić, Danijel, 2018. "A note on joint functional convergence of partial sum and maxima for linear processes," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 42-46.
    • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:42-46
    DOI: 10.1016/j.spl.2018.02.063
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    Cited by:

    1. Danijel Krizmanić, 2022. "Maxima of linear processes with heavy‐tailed innovations and random coefficients," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 238-262, March.

    More about this item

    Keywords

    Functional limit theorem; Regular variation; Stable Lévy process; Extremal process; M2 topology; Linear process;
    All these keywords.

    JEL classification:

    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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