Hamilton filter
Problems
The Hamilton filter suffers from a number of issues
- It amplifies cycles of various frequencies unevenly
- The extracted trend is noisy, rather than smooth
These flaws are made most clear via spectral analysis, a la @quastReliableRealTimeOutput2022 and @canovaFAQHowExtract:
Spectral analysis clarifies a number of issues
- Within the typical business cycle frequency range (6-32 quarters), cycles of various lengths are treated very differently
- Various high frequencies (cycles of less than 6 quarters) are allowed through the filter
Interesting idea: multivariate Hamilton filter
- Same as standard filter, but use multiple variables to forecast
- ”Trend” is simply the forecasted outcome, cycle is the residual
- Essentially a local projection