Two tools for extracting trend and cycle components from time-series data are:

• The Hodrick-Prescott filter, which extracts the TREND component from time-series data and leaves the CYCLE, SEASONAL and IRREGULAR components behind
• The Baxter-King method, which extracts the CYCLE component from time-series data and leaves the TREND, SEASONAL and IRREGULAR components behind

For the HP filter, values of lambda depend on the frequency of the data: the more frequent, the higher the lambda:

1. Annual: 100
2. Quarterly: 1600
3. Monthly: 14400

Both methods use centered moving averages (CMAs), so the values at the very beginning and very end of the extracted series will not mean much. The Baxter-King method cuts 3 years’ worth of data from the beginning and end of the extracted series.