Parameter Estimation for First-Order Bifurcating Autoregressive Processes with Point Process Technique

• Activity Number: 431
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Chenhua Zhang*+
• Companies: University of Southern Mississippi
• Keywords: bifurcating autoregressive processes ; Point process ; Weibull distribution

Abstract

We study the first-order bifurcating autoregressive processes with Weibull type innovations, i.e. $X_t=\phi X_{\lfloor t/2\rfloor}+\epsilon_t,$ where $\lfloor x \rfloor$ is the largest integer which does not exceed $x$, and $\{(\epsilon_{2t},\epsilon_{2t+1})\}$ is a sequence of independent and identically distributed (i.i.d.) random vectors with Weibull type distribution. The coefficient $\phi$ and tail index $\alpha$ are two parameters we are interested in. Using point process methods, we obtain the joint limit distribution of $(\hat{\phi}_n,\hat{\alpha})$.