Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors

Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter. Copyright 2005 Blackwell Publishing Ltd.