Mixing convergence of LSE for supercritical AR(2) processes with Gaussian innovations using random scaling

Mátyás Barczy (), Fanni Nedényi () and Gyula Pap
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Mátyás Barczy: Bolyai Institute, University of Szeged
Fanni Nedényi: Bolyai Institute, University of Szeged
Gyula Pap: Bolyai Institute, University of Szeged

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 6, No 5, 729-756

Abstract: 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.

Keywords: Autoregressive processes; Least squares estimator; Stable convergence; Mixing convergence; 62F12; 62H12; 60G15; 60F05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00184-023-00936-y

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