Implementing mixed-data sampling models for temporal sampling and aggregation in Stata

Many economic forecasts are constructed for temporally aggregated variables, such as monthly averages or quarterly sums, even when high-frequency data are available. Recent work on temporal aggregation shows that using only monthly or quarterly data can substantially reduce forecast accuracy and distort forecast evaluation. This presentation shows how Stata users can exploit high-frequency information using mixed-data sampling (MIDAS) methods. I first demonstrate how unrestricted MIDAS and restricted MIDAS can be implemented in Stata using existing data-management and time-series commands. These methods are straightforward to code and produce large gains relative to monthly or quarterly benchmarks, but they recover only part of the efficiency available from high-frequency information. I then show how to implement bottom-up MIDAS (BUMIDAS) methods. BUMIDAS reduces the number of parameters by up to a factor equal to the aggregation frequency and is the direct-forecast equivalent of optimal recursive bottom-up approaches. In the applications, daily recursive methods and bottom-up MIDAS reduce forecast errors by roughly half relative to standard monthly or quarterly approaches, and BUMIDAS often outperforms recursive methods in practice. Prototype Stata code is provided to automate aggregation, lag construction, estimation, forecasting, and forecast comparison across low-frequency, UMIDAS, RMIDAS, recursive bottom-up, and bottom-up MIDAS methods.