I'd like to use a Linear Dynamical System to model economic time series (e.g. Total Non-Farm Payroll), as observed in economic releases from the BLS, BEA, etc.
There are two stylized facts about the statistical releases I'd like to incorporate into the model:
- The first observation of a monthly period is released after the period is over, sometimes with up to 1 month of lag from the end of the observed period.
- There are often one to two more "revisions" of prior periods released at the same time.
Question: how do I apply filtering and smoothing in the presence of reporting lags and revisions? My first thought was to change the random variables to be vectors (one dimension for each lag) vs. scalars, but I'm not sure where to go from there. My specific confusion is about how an updated observation of a lagged period ends up influencing (via the observation matrix) my inference about the current period hidden state. The best I can come up with is that the observation matrix somehow needs to reflect both a) the observation error and b) the state transition matrix between the current period hidden state and the period revised (so that we can properly infer what a new observation for period t-2 means about period t-2, period t-1, and period t).