Least-squares estimation for bifurcating autoregressive processes

Bifurcating autoregressive processes are used to model each line of descent in a binary tree as a standard AR(p) process, allowing for correlations between nodes which share the same parent. Limit distributions of the least-squares estimators of the model parameters for a pth-order bifurcating autoregressive process (BAR(p)) are derived. An application to bifurcating integer-valued autoregression is given. A Poisson bifurcating model is introduced.