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

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

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.

Suggested Citation

  • Douissi, Soukaina & Es-Sebaiy, Khalifa & Alshahrani, Fatimah & Viens, Frederi G., 2022. "AR(1) processes driven by second-chaos white noise: Berry–Esséen bounds for quadratic variation and parameter estimation," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 886-918.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:886-918
    DOI: 10.1016/j.spa.2020.02.007
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    References listed on IDEAS

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    1. Es-Sebaiy, Khalifa & Viens, Frederi G., 2019. "Optimal rates for parameter estimation of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3018-3054.
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