An overview on models for tree-indexed time series

Abstract

Time series models indexed by a tree structure have recently been popular in the field of cell lineage studies and branching processes. This article aims to overview various models in a unified way, and thus providing some perspectives to the future works in this area. Three components are discussed in modeling tree-indexed time series. First component is the nature of trees indexing the data and the specification of the time series models defined on the tree may be the second component. The correlation between sisters sharing the same mother is referred to as the branching correlation and the mathematical specification of the branching correlation is regarded as the third component in modeling tree-indexed time series. We provide recent references with explanations of the three components in a broader context.