The Hodrick-Prescott filter applied to seasonally adjusted series has become a paradigm for business-cycle estimation at many economic agencies and institutions. We show that the filter can be obtained from MMSE estimation of the components in an unobserved component model, where the original...

Filters used to estimate unobserved components in time series are often designed on a priori grounds, so as to capture the frequencies associated with the component. A limitation of these filters is that they may yield spurious results. The danger can be avoided if the so called ARIMA model...