Modeling With Mixed-Frequency Data

Here's a bit more related to the FRB St. Louis conference.

The fully-correct approach to mixed-frequency time-series modeling is: (1) write out the state-space system at the highest available data frequency or higher (e.g., even if your highest frequency is weekly, you might want to write the system daily to account for different numbers of days in different months), (2) appropriately treat most of the lower-frequency data as missing and handle it optimally using the appropriate filter (e.g., the Kalman filter in the linear-Gaussian case).  My favorite example (no surprise) is here.  

Until recently, however, the prescription above was limited in practice to low-dimensional linear-Gaussian environments, and even there it can be tedious to implement if one insists on MLE.  Hence the well-deserved popularity of the MIDAS approach to approximating the prescription, recently also in high-dimensional environments.     

But now the sands are shifting.  Recent work enables exact Bayesian posterior mixed-frequency analysis even in high-dimensional structural models.  I've known Schorfheide-Song (2015, JBES; 2013 working paper version here) for a long time, but I never fully appreciated the breakthrough that it represents -- that is, how straightforward exact mixed-frequency estimation is becoming --  until I saw the stimulating Justiniano presentation at FRBSL (older 2016 version here).  And now it's working its way into important substantive applications, as in Schorfheide-Song-Yaron (2017, forthcoming in Econometrica).