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However, due to effects that accumulate over long time windows and interventions that have complex evolution, a lack of robust inference tools has limited the widespread applicability of such $ N $-of-1 designs. This work combines techniques from experimental design in causal inference and system identification from control theory to provide such an inference framework. We derive a model of the dynamic interference effect that arises in linear time-invariant dynamical systems. We show that a family of causal estimands analogous to those studied in potential outcomes are estimable via a standard estimator derived from the method of moments. We derive formulae for higher moments of this estimator and describe conditions under which $ N $-of-1 designs may provide faster ways to estimate the effects of interventions in dynamical systems. We also provide conditions under which our estimator is asymptotically normal and derive valid confidence intervals for this setting.<\/jats:p>","DOI":"10.1093\/biomet\/asaf013","type":"journal-article","created":{"date-parts":[[2025,2,15]],"date-time":"2025-02-15T15:14:33Z","timestamp":1739632473000},"source":"Crossref","is-referenced-by-count":5,"title":["Randomization inference when N equals one"],"prefix":"10.1093","volume":"112","author":[{"suffix":"By","given":"Tengyuan","family":"Liang","sequence":"first","affiliation":[{"name":"Econometrics and Statistics, Booth School of Business, The University of Chicago , 5807 S. 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