Online Targeted Learning for Time Series
We consider the case that we observe a time series where at each time we observe in chronological order a covariate vector, a treatment, and an outcome. We assume that the conditional probability distribution of this time specific data structure, given the past, depends on the past through a fixed (in time) dimensional summary measure, and that this conditional distribution is described by a fixed (in time) mechanism that is known to be an element of some model space (e.g., unspecified). We propose a causal model that is compatible with this statistical model and define a family of causal effects in terms of stochastic interventions on a subset of the treatment nodes on a future outcome, and establish identifiability of these causal effects from the observed data distribution.
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