Dynamic Factor Analysis with Nonlinear Temporal Aggregation Constraints

The paper estimates an index of coincident economic indicators for the U.S. economy using time series with different frequencies of observation (monthly and quarterly, possibly with missing values). The model considered is the dynamic factor model proposed by Stock and Watson, specified in the logarithms of the original variables and at the monthly frequency, which poses a problem of temporal aggregation with a nonlinear observational constraint when quarterly time series are included. Our main methodological contribution is to provide an exact solution to this problem, that hinges on conditional mode estimation by extended Kalman filtering and smoothing. On the empirical side the contribution of the paper is to provide monthly estimates of quarterly indicators, among which Gross Domestic Product, that are consistent with the quarterly totals.