Mixing convergence of LSE for supercritical AR(2) processes with Gaussian innovations using random scaling
Statistics Theory
2025-09-16 v3 Probability
Statistics Theory
Abstract
We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with Gaussian innovations having real characteristic roots with different absolute values. We use an appropriate random scaling such that the limit distribution is a two-dimensional normal distribution concentrated on a one-dimensional ray determined by the characteristic root having the larger absolute value.
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Cite
@article{arxiv.2101.01590,
title = {Mixing convergence of LSE for supercritical AR(2) processes with Gaussian innovations using random scaling},
author = {Matyas Barczy and Fanni Nedényi and Gyula Pap},
journal= {arXiv preprint arXiv:2101.01590},
year = {2025}
}
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37 pages