Asymptotic results for random coefficient bifurcating autoregressive processes

2012/04/13 by Vassili Blandin, Blandin, Vassili
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F05 #60F15 #60G42 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1204.2926

openalex publication_date 2012/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.

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