A Rademacher-Menchov approach for random coefficient bifurcating autoregressive processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Bercu, Bernard¹  Blandin, Vassili¹ 

[1] Univ Bordeaux, Inst Math Bordeaux, UMR CNRS 5251, F-33405 Talence, France

关键词: Bifurcating autoregressive process;    Random coefficient;    Least squares;    Martingale;    Almost sure convergence;    Central limit theorem;   

DOI  :  10.1016/j.spa.2014.10.006

来源: Elsevier

【 摘 要 】

We investigate the asymptotic behavior of the least squares estimator of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on inherited and environmental effects, we establish the almost sure convergence of our estimates. In addition, we also prove a quadratic strong law and central limit theorems. Our approach mainly relies on asymptotic results for vector-valued martingales together with the well-known Rademacher-Menchov theorem. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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