Law of the iterated logarithm for error variance estimator in pth-order non linear autoregressive processes

Kaiyu Liang and Yong Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 17, 5673-5686

Abstract: In this article, under some suitable assumptions, using Taylor expansion, the Borel-Cantelli lemma and the classical Hartman and Wintner law of the iterated logarithm for independent random variables, the law of the iterated logarithm for the error variance estimator in the pth-order non linear autoregressive processes with independent and identically distributed errors is established. Two examples, first-order autoregressive processes (AR(1)) and self-exciting threshold autoregressive (SETAR) processes, are given to verify the results.

Date: 2025
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DOI: 10.1080/03610926.2024.2443691

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