Short-term and long-term trends, seasonal and the business cycle

We consider business cycle estimation with Hodrick-Prescott (HP)-type filters. We address, first, the well-known criticism of spurious results due to the ad-hoc character of the filter, and the (often ignored yet important) limitation implied by revisions, which produce imprecision in the cycle estimator for recent periods. We show how the integration of some relatively simple ARIMA-model-based (AMB) techniques with HP filtering can produce important improvements in the performance of the cyclical signal. Finally, the complete procedure of applying the HP filter to a "clean" series is presented within a model-based methodology. This AMB methodology displays several nice features. First, it incorporates automatically optimal treatment of end points and provides a cleaner cyclical signal. Second, it provides an internally consistent full decomposition of the series into "trend + cycle + seasonal irregular" components, where the trend plus cycle aggregate into the standard trend-cycle component of the AMB decomposition. Third, the method is based on the AMB approach, that is, it starts with the ARIMA model for the series, which can be directly identified from the data. In this way, misspecification errors and spurious results are avoided. The procedure consists of straightforward minimum mean squared error estimation of unobserbed components, modeled as ARIMA processes, which aggregate into the model identified for the observed series. The models for the trend-cycle, seasonal and irregular ccomponents are thus determined from the observed series model. The splitting of the trend-cycle into a trend plus a cycle depends on the choice of the HP-filter parameter A,. Given this parameter, the complete decomposition is then fully determined. An additional advantage is that the parametric model-based procedure provides a convenient framework for diagnostics and inference.