Identifiability by common backdoor in summary causal graphs of time series

The identifiability problem for interventions aims at assessing whether the total e ffect of some given interventions can be written with a do-free formula, and thus be computed from observational data only. We study this problem, considering multiple interventions and multiple e ff ects, in the context of time series when only abstractions of the true causal graph in the form of summary causal graphs are available. We focus in this study on identifiability by a common backdoor set, and establish, for time series with and without consistency throughout time, conditions under which such a set exists. We also provide algorithms of limited complexity to decide whether the problem is identifiable or not.