Asymptotic results for random coefficient bifurcating autoregressive processes

TL;DR

This paper investigates the asymptotic properties of estimators in random coefficient bifurcating autoregressive processes, establishing convergence, strong laws, and central limit theorems under certain assumptions.

Contribution

It provides new asymptotic results for estimators in bifurcating autoregressive models with random coefficients, using martingale limit theorems.

Findings

Almost sure convergence of estimators

Quadratic strong law established

Central limit theorems proven

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.