With the proliferation of mobile devices and the internet of things, developing principled solutions for privacy in time series applications has become increasingly important. While differential privacy is the gold standard for database privacy, many time series applications require a different kind of guarantee, and a number of recent works have used some form of inferential privacy to address these situations. However, a major barrier to using inferential privacy in practice is its lack of graceful composition -- even if the same or related sensitive data is used in multiple releases that are safe individually, the combined release may have poor privacy properties. In this paper, we study composition properties of a form of inferential privacy called Pufferfish when applied to time-series data. We show that while general Pufferfish mechanisms may not compose gracefully, a specific Pufferfish mechanism, called the Markov Quilt Mechanism, which was recently introduced, has strong composition properties comparable to that of pure differential privacy when applied to time series data.