Preliminary Identification of Branching-Heteroscedasticity for Tree-Indexed Autoregressive Processes

Sharpness of second moment criteria for branching and tree-indexed processes

A class of branching processes in varying environments is exhibited which become extinct almost surely even though the means Mn grow fast enough so that ∑ M−1 n is finite. In fact, such a process is constructed for every offspring distribution of infinite variance, and this establishes the converse of a previously known fact: that if a distribution has finite variance then ∑ M−1 n = ∞ is equiva...

Model Identification for Infinite Variance Autoregressive Processes

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside...

Explicit Equations for ACF in Autoregressive Processes In the Presence of Heteroscedasticity Disturbances

A Preliminary Investigation of Transport-branching Processes

Tree Indexed Markov Processes and Long Range Dependency

This paper describes the second order statistics of a finite state Markov process indexed on a binary tree. Such models are the discrete state analogues of the continuous state Gauss-Markov processes as described by Basseville et al [I]. Such processes are termed tree-indexed processes. The idea is to use the leaf nodes of the tree at a specified depth, as indices for a time series, and to deri...