Random coefficients bifurcating autoregressive processes

TL;DR

This paper introduces a novel asymmetric bifurcating autoregressive model with random coefficients, coupled with a Galton Watson tree, and develops consistent, asymptotically normal estimators for its parameters.

Contribution

It proposes a new model combining bifurcating autoregression with random coefficients and missing data handling, along with rigorous estimation theory.

Findings

Proposed least-squares estimators are consistent.

Established asymptotic normality of estimators.

Derived new results in bifurcating Markov chain and martingale frameworks.

Abstract

This paper presents a model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency with a convergence rate, and their asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new important general results in both these frameworks.