March 2022 A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations
Danijel Krizmanić
Author Affiliations +
Braz. J. Probab. Stat. 36(1): 138-156 (March 2022). DOI: 10.1214/21-BJPS520

Abstract

Recently a functional limit theorem for sums of moving averages with random coefficients and i.i.d. heavy tailed innovations has been obtained under the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series. The convergence takes place in the space D[0,1] of càdlàg functions with the Skorohod M2 topology. In this article, we extend this result to the case when the innovations are weakly dependent in the sense of strong mixing and local dependence condition D.

Funding Statement

This work has been supported in part by University of Rijeka research grants uniri-prirod-18-9 and uniri-pr-prirod-19-16 and by Croatian Science Foundation under the project IP-2019-04-1239.

Acknowledgments

The author would like to thank the anonymous referees for comments and suggestions which helped to improve the paper.

Citation

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Danijel Krizmanić. "A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations." Braz. J. Probab. Stat. 36 (1) 138 - 156, March 2022. https://doi.org/10.1214/21-BJPS520

Information

Received: 1 February 2020; Accepted: 1 September 2021; Published: March 2022
First available in Project Euclid: 6 February 2022

MathSciNet: MR4377126
zbMATH: 1490.60071
Digital Object Identifier: 10.1214/21-BJPS520

Keywords: Functional limit theorem , M2 topology , Moving average process , regular variation

Rights: Copyright © 2022 Brazilian Statistical Association

Vol.36 • No. 1 • March 2022
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