1988issue C111-3
Fourier cycles versus calendar seasonal regimes
A Fourier reconstruction of summed sines sits beside weekday, month-start, and four-year political-term windows so a student can test whether a trend-adjusted political-term composite is a recovered dominant cycle or a separate dated seasonal regime.
- Fourier analysis recovers separate sinusoidal components, each with its own period and amplitude, that can be added together to reconstruct an observed price curve.
- When underlying cycles were ranked by crest amplitude, every listed cycle except a 46-year component was reported as statistically significant.
- Calendar timing was treated as a usable cycle layer: Mondays typically weaker, Fridays typically stronger, and the first three days of a month with a stronger historical record.
- After trend adjustment, a four-year political-term composite was weaker in the first half of the election year, stronger in the second half, and placed its trough in the middle of the second post-election year.
Two readings of one price path
Fourier analysis, in the archive sense, recovers an ordered price path as summed sine waves that differ in period and amplitude. Seasonal analysis reads weekday, month-start, and multi-year political-term windows as dated market regimes rather than as fitted sines.
The archive kept both readings. One recovers periodic components that can be added back into the observed curve. The other locks events to the calendar and stacks like-dated stretches after long-run drift is removed.
Sine waves and ranked dominant cycles
Fourier analysis recovers separate sinusoidal components, each with its own period and amplitude. Those components can be added together to reconstruct an observed price curve.
A dominant cycle is an underlying periodic component ranked by crest amplitude and checked for statistical significance. When underlying cycles were ranked by amplitude at the crest, every listed cycle except a 46-year component was reported as statistically significant.
Dated weekday and month-start windows
Calendar timing was treated as a usable cycle layer, not as another fitted sine. Mondays were described as typically weaker, Fridays as typically stronger, and the first three days of a month as having a stronger historical record.
Those windows stay on the calendar side of the comparison. They are dated regimes: a weekday, a month-start, or a multi-year political-term span, not a period recovered from the price path.
A trend-adjusted presidential-term window
A presidential-term window is a four-year span cut into successive three-month blocks so election-year and post-election phases can be stacked. The archive composite used 24 terms starting in 1886, split each term into 16 three-month blocks, averaged the percent change in each block, and then corrected those averages for trend.
A trend-adjusted composite averages like-dated percent changes after long-run drift is removed so repeated terms can be compared. In that trend-adjusted average, election-year prices were weaker across the first six months and stronger across the second six months. The same composite continued lower for a year and a half after the election and placed its trough in the middle of the second post-election year.
Election-year months on the rise-share profile
A monthly seasonal profile was built as the share of observations in which prices rose, plotted around a 56 percent mean and bounded by one-standard-deviation bands.
On that monthly profile, October and November of the election year stood above typical months, December in election years sat near the mean, and the February after the election marked the start of a weaker stretch.
An editorial test after trend is removed
Editorial: once the trend-adjusted composite is in hand, the Fourier column still holds only the summed sines and the cycles ranked by crest amplitude. The calendar column holds the weekday, month-start, monthly rise-share, and presidential-term windows.
Editorial: a student can then ask whether the stacked political-term shape is the same object as a recovered dominant cycle, or a separate dated seasonal regime that appears only after like-dated blocks are averaged and trend is taken out.
All readings on this track · 26 readings
- 1982Critiquing Fourier, Elliott, and seasonal commodity models
- 1982Evaluating half-hour crossovers with cycle priors and stops
- 1984Building moving-window spectral cycle forecasts
- 1988Fourier cycles versus calendar seasonal regimes
- 1989Constructing analog cycle signatures from price lows
- 1990Curve fits fail the forecast test
- 1991Auditing moving-average length with Fourier spectra
- 1991Closed-form phase for dominant-cycle spectra
- 1993Evaluating windowed spectral forecasts of index turning points
- 1994Window length for moving-window spectral forecasts
- 1994Constructing WAMI power and phase spectra
- 1994Fourier-tuned momentum filter design
- 1994Aliasing, leakage, and dominant-cycle reads from sampled prices
- 1995Constructing indicator lookbacks from Fourier spectra
- 1996Constructing phase from a dominant-cycle sine and cosine pair
- 1999Sinusoidal pseudo-securities for indicator evaluation
- 2000Constructing dominant cycle length from Hilbert phase
- 2000Constructing adaptive channel breakouts from a measured cycle period
- 2005Embedding forex prices into a singular-spectrum forecast basis
- 2005Constructing recurrent forecasts from grouped spectral components
- 2007Constructing a dominant cycle from transformed Fourier spectra
- 2010Why cycle indicators fail when parameters shift
- 2019Constructing futures momentum as open-interest-scaled rate of change
- 2019Judging a dominant cycle and a trend filter by sample, lag and the move they keep
- 2020Constructing futures turnover time and urgency
- 2020Stock power ratio as a growth trend filter