Graphical modeling of stochastic processes driven by correlated errors

TL;DR

This paper introduces a graphical framework for modeling stochastic processes with correlated errors, characterizes equivalence classes of such graphs, and discusses computational complexity and specific process cases.

Contribution

It develops a new graphical modeling approach for stochastic processes with correlated errors, including characterizations of equivalence and complexity analysis.

Findings

Characterization of graph equivalence classes for local independence structures.

Deciding Markov equivalence is coNP-complete.

Proven global Markov property for multivariate Ornstein-Uhlenbeck processes.

Abstract

We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolynomially as a function of the size of the node set in the graph. We show that deciding Markov equivalence is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.