We construct a state space model for measuring real economic activity in real time (e.g., minute by minute) using a variety of stock and flow data, observed at mixed frequencies. Our data set comprises macroeconomic and financial variables: GDP, IP, unemployment, stock and bond market data, and interest rates, among others. The main difficulties in defining our state space relate to the use of mixed frequencies and the presence of both stock and flow data. Macroeconomic variables, as we know, have a lower frequency than financial variables and hence display a missing observation problem at the higher frequency. Moreover many macroeconomic variables are flow variables that need to be properly aggregated, with the problem that, for example, every quarter we observe what is consumed/produced/invested during the quarter without additional information about how much of it is consumed/produced/invested in a single month, day or minute of the quarter. We construct a state space model that is able to handle both difficulties. We clarify the issues associated with exact optimal filtering in such environments, and we propose a model that permits exact filtering. We apply our methods to the U.S. economy, conducting the estimation using parallel computing, and compare them to competitors
