We present a method for "ecological inference", learning individual-level associations from aggregate data for time series data. This problem has recently been highlighted with the COVID-19 pandemic where demographic time series data is difficult to obtain while aggregate time series data is easily obtainable. It is not unreasonable to expect at least a small amount of reported data for component time series, so our approach uses that assumption to create a transition matrix element-wise to be used in a constrained Kalman filter to be used on other aggregate time series. We consider the COVID-19 pandemic case numbers between states and regions within the states to help us estimate time series data in other states, and our results show a significant degree of accuracy to the actual case numbers in those regions.