Almost Sure Central Limit Theorem for Error Variance Estimator in Pth-Order Nonlinear Autoregressive Processes

Kaiyu Liang and Yong Zhang ()
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Kaiyu Liang: School of Mathematic, Jilin University, Changchun 130012, China
Yong Zhang: School of Mathematic, Jilin University, Changchun 130012, China

Mathematics, 2024, vol. 12, issue 10, 1-16

Abstract: In this paper, under some suitable assumptions, using the Taylor expansion, Borel–Cantelli lemma and the almost sure central limit theorem for independent random variables, the almost sure central limit theorem for error variance estimator in the pth-order nonlinear autoregressive processes with independent and identical distributed errors was established. Four examples, first-order autoregressive processes, self-exciting threshold autoregressive processes, threshold-exponential AR progresses and multilayer perceptrons progress, are given to verify the results.

Keywords: almost sure central limit theorem; nonlinear autoregressive processes; error variance estimator; residuals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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