Time Aggregation and the Hodrick-Prescott Filter

The time aggregation properties of the Hodrick-Prescott (HP) filter to decompose a time series into trend and cycle are analized for the case of annual, quarterly, and monthly data. It is seen that aggregation of the disagreggate component estimators cannot be obtained as the exact result from applying an HP filter to the aggregate series (and viceversa).time series, estimators, business cycles