Asymptotics of an Extreme-Value Estimator for a First-Order Bifurcating Autoregressive Process with an Unknown Location Parameter
Andrew Bartlett
Southern Illinois University Edwardsville
Asymptotics of an alternative extreme-value estimator for the autocorrelation parameter in a first-order bifurcating autoregressive (BAR) process with non-gaussian innovations are derived. This contrasts with traditional estimators whose asymptotic behavior depends on the central part of the innovation distribution. Within any BAR model, the main concern is addressing the complex dependency between generations. The inability of traditional methods to handle this dependency motivated an alternative procedure. Our interest lies in investigating through simulation how significant the dependency between generations really is. Additionally, we will investigate the asymptotic properties of our extreme value estimator associated with the BAR(1) model with non-gaussian innovations. Finally, the implications of our extreme value approach are discussed with an extensive simulation study that not only asses the reliability of our proposed estimate but presents the findings for a new estimator of an unknown location parameter θ and its implications.