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Time-varying relationships and volatility are two methodological challenges that are particular to the field of time series. In the case of the former, more comprehensive understanding can emerge when we ask under what circumstances relationships may change. The impact of context—such as the political environment, the state of the economy, the international situation, etc.—is often missing in dynamic analyses that estimate time-invariant parameters. In addition, time-varying volatility presents a number of challenges including threats to inference if left unchecked. Among time-varying parameter models, the Dynamic Conditional Correlation (DCC) model is a creative and useful approach that deals effectively with over-time variation in both the mean and variance of time series. The DCC model allows us to study the evolution of relationships over time in a multivariate setting by relaxing model assumptions and offers researchers a chance to reinvigorate understandings that are tested using time series data. We demonstrate the method's potential in the first example by showing how the importance of subjective evaluations of the economy are not constant, but vary considerably over time as predictors of presidential approval. A second example using international dyadic time series data shows that the story of movement and comovement is incomplete without an understanding of the dynamics of their variance as well as their means.