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Design and Analysis of Time Series Experiments develops a comprehensive set of models and methods for drawing causal inferences from time series. Example analyses of social, behavioral, and biomedical time series illustrate a general strategy for building AutoRegressive Integrated Moving Average (ARIMA) impact models. The classic Box-Jenkins-Tiao model-building strategy is supplemented with recent auxiliary tests for transformation, differencing, and model selection. The validity of causal inferences is approached from two complementary directions. The four-validity system of Cook and Campbell relies on ruling out discrete threats to statistical conclusion, internal, construct, and external validity. The Rubin system causal model relies on the identification of counterfactual time series. The two approaches to causal validity are shown to be complementary and are illustrated with a construction of a synthetic control time series. Example analyses make optimal use of graphical illustrations. Mathematical methods used in the example analyses are explicated in technical appendices, including expectation algebra, sequences and series, maximum likelihood, Box-Cox transformation analyses and probability.