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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:150

Article

Douissi, Soukaina¹  Es-Sebaiy, Khalifa²  Alshahrani, Fatimah³  Viens, Frederi G.⁴ 

[1] Cadi Ayyad Univ, Fac Semlalia, Lab LIBMA, Marrakech 40000, Morocco

[2] Kuwait Univ, Fac Sci, Dept Math, Kuwait, Kuwait

[3] Princess Nourah bint Abdulrahman Univ, Dept Math Sci, Riyadh, Saudi Arabia

[4] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

关键词: Central limit theorem;    Berry-Ess?en;    Malliavin calculus;    Parameter estimation;    Time series;    Wiener chaos;   

DOI  :  10.1016/j.spa.2020.02.007

来源: Elsevier

【 摘 要 】

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.(C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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