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Dramatic world change has stimulated interest in research questions about the dynamics of politics. We have seen increases in the number of time series data sets and the length of typical time series. But three shortcomings are prevalent in published time series analysis. First, analysts often estimate models without testing restrictions implied by their specification. Second, researchers link the theoretical concept of equilibrium with cointegration and error correction models. Third, analysts often do a poor job of interpreting results. The consequences include weak connections between theory and tests, biased estimates, and incorrect inferences. We outline techniques for estimating linear dynamic regressions with stationary data and weakly exogenous regressors. We recommend analysts (1) start with general dynamic models and test restrictions before adopting a particular specification and (2) use the wide array of information available from dynamic specifications. We illustrate this strategy with data on Congressional approval and tax rates across OECD countries. [ABSTRACT FROM AUTHOR]