2002issue C071
Timing market cycles with finite impulse response filters and FFT
After a technology-heavy peak and a decline that had not yet reversed, the recovery question is framed as cycle timing. Isolate the dominant rhythm first, then ask whether a near-zero-lag finite impulse response smoother and a Fourier spectrum mark the same turn.
- Boom-and-bust sequences, including the early-2000 technology-heavy peak and unfinished decline, are treated as cycle-timing material rather than a search for a settled cause.
- The cycle-cause debate lists profits, interest-rate swings, and inflation as candidates, yet leaves both the cause and the existence of cycles contested.
- A finite impulse response filter is applied as a finite-length smoother whose aim is zero-lag smoothing, so the cycle mark is not postponed by the smoother.
- A fast Fourier transform supplies the spectral reading of candidate cycles, and the dominant cycle is the strongest rhythm used as the timing reference.
A recovery question after a boom and bust
Historical equity prices are described as repeating boom-and-bust sequences. A technology-heavy index peaked in early 2000 and then declined, and that decline had not yet reversed.
Comparable boom-then-collapse sequences are cited for a major US industrial average before 1929 and for a major Japanese equity index in the 1980s.
More than two years after the early-2000 peak, the question of when prices might recover is framed as a cycle-timing problem rather than a puzzle that first requires a settled cause.
The cycle-cause debate is left open
Corporate profits, interest-rate swings, and inflation are listed as candidate contributors to market cycles. The existence of those cycles remains contested among analysts.
That cycle-cause debate is not settled here. The practical stance offered is to isolate the dominant cycle in observed prices and time entries and exits with analytical tools instead of waiting for an explanation of why the cycle occurs.
Agree on the turn before adding a story
A dominant cycle is the strongest recurring rhythm isolated from a price, volume, or breadth series and used as the reference period for timing.
Finite impulse response filters are introduced as finite-length smoothers applied to ordered prices so a cycle turn can be marked with as little delay as the filter design allows. Zero-lag smoothing is the design aim: the filter should track the underlying series closely enough that the smoother itself does not postpone a cycle turn.
The fast Fourier transform is introduced as a more complex spectral method. It decomposes an ordered market series into frequency components so candidate cycles can be read from the spectrum.
Editorial: a turn is treated as identified only when the near-zero-lag smoother and the spectrum point to the same rhythm. Identified market cycles and trends are characterized as leading signals of broader business conditions.
All readings on this track · 10 readings
- 1982An odd-length smoother from a cycle cutoff
- 1989Smoothing filters, cutoff, poles, and sample delay
- 1992Constructing a cycle-aware finite impulse response detrender
- 2002Rebuild a smoother by writing the lag into the coefficients
- 2002Timing market cycles with finite impulse response filters and FFT
- 2002Constructing the relative strength index with an even-order finite-impulse-response prefilter
- 2003Recursive and cascaded moving-average construction
- 2006One second-order transfer function, a family of trend filters
- 2019Constructing the Voss line from a bandpass and a short FIR sum
- 2020Truncated bandpass construction as a finite-length trend filter