Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

TL;DR

This paper investigates the asymptotic properties of least squares estimators in bifurcating autoregressive processes, establishing convergence and distributional results under weak noise assumptions using martingale techniques.

Contribution

It introduces a novel martingale-based approach to analyze the asymptotic behavior of estimators in bifurcating autoregressive models under minimal noise assumptions.

Findings

Almost sure convergence of estimators

Quadratic strong law established

Central limit theorem proven for estimators

Abstract

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.