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.

TR Number: 
J. Zhou and I.V. Basawa
Key Words: 
Bifurcating autoregression, exponential innovations, maximum likelihood, exact distribution, limit distribution, non-standard asymptotics

To request a copy of this report, please email us. We will send you a pdf copy if one is available.