Discussion paper Series 1 / Volkswirtschaftliches Forschungszentrum der Deutschen Bundesbank 2005,19
This paper discusses various approaches to decompose economic time series into their trend and cyclical components. For over 30 years now, the Deutsche Bundesbank publishes trend-adjusted indicators in its Statistical Supplement 4 entitled ?Seasonally Adjusted Business Statistics? which are calculated basically as unweighted moving averages. As alternatives to the Bundesbank?s current approach, the widely used Hodrick-Prescott filter, the extended exponential smoothing filter and the Baxter-King low-pass filter are investigated. All three of the filters are able to clearly separate the trend component from the cyclical component for German economic indicators. The turning points of the growth cycles are largely consistent with the Bundesbank?s current approach. However, the trend deviation level at the end of the series is still subject to noticeable changes. This uncertainty can be quantified with the help of ARIMA forecasts. The choice of filter ultimately depends on the features of the time series to be filtered. Whereas extended exponential smoothing is well suited to I(1) processes, the Hodrick-Prescott filter is preferable for I(2) series.
Business cycle trend time-series analysis Hodrick-Prescott