Identifiability of total effects from abstractions of time series causal graphs

We study the problem of identifiability of the total effect of an intervention from observational time series only given an abstraction of the causal graph of the system. Specifically, we consider two types of abstractions: the extended summary causal graph which conflates all lagged causal relations but distinguishes between lagged and instantaneous relations; and the summary causal graph which does not give any indication about the lag between causal relations. We show that the total effect is always identifiable in extended summary causal graphs and we provide necessary and sufficient graphical conditions for identifiability in summary causal graphs. Furthermore, we provide adjustment sets allowing to estimate the total effect whenever it is identifiable.