PhD Student, DLR Jena
Causal inference in time and frequency on process graphs
Structural vector autoregressive (SVAR) processes model the joint behaviour of processes that evolve over a discrete set of time points and influence each other linearly through both immediate and delayed effects. An SVAR process can be thought of as a linear model for an infinite time series graph, where a vertex represents the state of a process at a given time and a directed link indicates a direct immediate or delayed effect between processes. The potentially highly complex time series graph can be reduced to a finite graph, called the process graph, where two processes are connected by a directed link whenever there is an immediate or delayed effect between them. In this talk I explain how an SVAR process can be formulated as a structural causal model of stochastic processes on the process graph.
This formulation leads to a generalised trek rule by which the process graph dictates algebraic relations between entries in the spectral density, i.e. the frequency domain analogue of the autocovariance. With this trek rule, it is possible to reason combinatorially and algebraically about the frequency domain causal structure of SVAR processes at the level of the finite process graph rather than the infinite time series graph.