AR(1) processes driven by second-chaos white noise: Berry–Esséen bounds for quadratic variation and parameter estimation

Soukaina Douissi, Khalifa Es-Sebaiy, Fatimah Alshahrani and Frederi G. Viens

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 886-918

Abstract: In this paper, we study the asymptotic behavior of the quadratic variation for the class of AR(1) processes driven by white noise in the second Wiener chaos. Using tools from the analysis on Wiener space, we give an upper bound for the total-variation speed of convergence to the normal law, which we apply to study the estimation of the model’s mean-reversion. Simulations are performed to illustrate the theoretical results.

Keywords: Central limit theorem; Berry–Esséen; Malliavin calculus; Parameter estimation; Time series; Wiener chaos (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2020.02.007

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