Lagged phase clocks for market cycles

Two delayed measurements

Inflation-adjusted monthly industrial-average levels were converted to logs so equal percentage moves occupy equal distance before any cycle measurement.

Editorial view: read the cycle as a delayed two-axis state. One axis is how far a double-smoothed series sits from a slow growth line. The other is how fast that gap is changing. A Fourier period then becomes a clock of late, early, and still-unconfirmed zones rather than a date to trade.

Dominant-cycle widths

Spectral inspection of that series located recurring periods near 41 months and near 13 months, which then set the double-smoothing widths for a long and a short motion. A dominant-cycle is a Fourier-identified recurring period used as the smoothing width for a long or short homeostatic motion.

Exponential-smoothing of level and speed

Exponential-smoothing, in this workflow, is repeated triangular moving averages that produce a double-smoothed level and a delayed velocity estimate so amplitude can be plotted against rate of change.

Long-cycle amplitude was the 41-month double-smoothed series minus a background real-growth line of about 1 percent a year. Velocity was monthly differences double-smoothed near 29 months and scaled to a yearly rate.

A clockwise phase-diagram

On the amplitude-versus-velocity plot the path always moved clockwise, with a larger swing drawing a larger loop and irregular price motion drawing an irregular loop. Homeostasis is that up-and-down motion, which keeps a circular phase structure even when the size, speed, and shape of each swing vary.

Phase-time on the lagged clock

An idealized phase clock placed the peak at 3:00, the trough at 9:00, the fastest rise at 12:00, and the fastest fall at 6:00, while noting those turning points are identified only after the averages become available. Editorial view: those hour marks locate late, early, and still-unconfirmed zones. They are not a calendar date for a trade.

Why the confirmed trace is late

Because the long-cycle velocity smoother needed about 29 months, the confirmed diagram lagged by about 70 months and the historical trace stopped near 1992. Phase-navigation is a trial estimate of the present point on a lagged diagram, used to read the risk of a swing before the moving averages are fully known.

A contrarian-strategy before the turn

The case-study navigation rule sold while the delayed clock still pointed before the peak, about 1:30 to 2:00, and bought while it still pointed before the trough, about 7:30 to 8:00, treating exact extremes as unknowable in real time. A contrarian-strategy here is that phase-clock rule: it marks sells while the delayed state still sits before a peak and buys only after the state has moved toward a trough, accepting that confirmation arrives after the turn.

Short-cycle state in mid-1987

Reconstructing the short-cycle state for mid-1987 placed it far to the right of the phase plot, which the study treated as a near-term downturn mark that the long-cycle state did not extend into a multi-year decline.

Series that do not fit

The same construction was described as poorly suited to noncyclical series, random walks, and single-name prices driven by firm- or industry-specific events.