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N-of-1 experiments, where a unit serves as its own control and treatment indifferent time windows, have been used in certain medical contexts for decades.However, due to effects that accumulate over long time windows andinterventions that have complex evolution, a lack of robust inference tools haslimited the widespread applicability of such N-of-1 designs. This work combinestechniques from experiment design in causal inference and system identificationfrom control theory to provide such an inference framework. We derive a modelof the dynamic interference effect that arises in linear time-invariantdynamical systems. We show that a family of causal estimands analogous to thosestudied in potential outcomes are estimable via a standard estimator derivedfrom the method of moments. We derive formulae for higher moments of thisestimator and describe conditions under which N-of-1 designs may provide fasterways to estimate the effects of interventions in dynamical systems. We alsoprovide conditions under which our estimator is asymptotically normal andderive valid confidence intervals for this setting.

Randomization Inference When N Equals One