Short-Term and Long-Term Trends, Seasonal Adjustment, and the Business Cycles.

In this monograph, first, we analyze in detail some of the major limitations of the standard procedure to estimate business cycles with the Hodrick-Prescott (HP) filter. By incorporating time series analysis techniques, it is seen how some intuitive and relatively simple modifications to the filter can improve significantly its performance, in particular in terms of cleanness of the signal, smaller revision, stability of end-period estimators, and detection of turning points. Then, we show how the modified filter can be seen as the exact solution of a well-defined statistical problem, namely, optimal (minimum mean squared error) estimation of components in a standard unobserved-component model, where the observed series is decomposed into a trend, a cycle, a seasonal, and an irregular component.