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Article

On Relative Stability for Strongly Mixing Sequences

by
Adam Jakubowski
and
Zbigniew Stanisław Szewczak
*
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
*
Author to whom correspondence should be addressed.
Foundations 2025, 5(4), 33; https://doi.org/10.3390/foundations5040033
Submission received: 30 July 2025 / Revised: 6 September 2025 / Accepted: 23 September 2025 / Published: 25 September 2025
(This article belongs to the Section Mathematical Sciences)
Versions Notes

Abstract

We consider a class of strongly mixing sequences with infinite second moment. This class contains important GARCH processes that are applied in econometrics. We show the relative stability for such processes and construct a counterexample. We apply these results and obtain a new CLT without the requirement of exponential decay of mixing coefficients, and provide a counterexample to this as well.
Keywords: relative stability; central limit theorem; α coefficient relative stability; central limit theorem; α coefficient

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MDPI and ACS Style

Jakubowski, A.; Szewczak, Z.S. On Relative Stability for Strongly Mixing Sequences. Foundations 2025, 5, 33. https://doi.org/10.3390/foundations5040033

AMA Style

Jakubowski A, Szewczak ZS. On Relative Stability for Strongly Mixing Sequences. Foundations. 2025; 5(4):33. https://doi.org/10.3390/foundations5040033

Chicago/Turabian Style

Jakubowski, Adam, and Zbigniew Stanisław Szewczak. 2025. "On Relative Stability for Strongly Mixing Sequences" Foundations 5, no. 4: 33. https://doi.org/10.3390/foundations5040033

APA Style

Jakubowski, A., & Szewczak, Z. S. (2025). On Relative Stability for Strongly Mixing Sequences. Foundations, 5(4), 33. https://doi.org/10.3390/foundations5040033

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