Dominant-cycle phase flips as regime tests

A missed turn is a regime test

Regime-dependence, in this setting, means the useful phase of a given cycle length depends on whether the market is in an advance regime or a corrective regime. Editorial reading: when a projected multi-year turning point fails to appear, treat the miss as a test of that regime, not as a broken clock.

When neither a cycle high nor a cycle low appears on a projected date, the same cycle can invert by about 180 degrees onto a later anniversary date. Those inversions often cluster near major trend changes. That reassignment is a phase-inversion: a roughly 180-degree reset of the high-low calendar after a projected turning point fails to appear.

Two calendars of one cycle length

A roughly 40.68-month cycle in a broad equity index can be drawn as two opposing calendars. The advance-aligned-calendar is the phase that has lined up with major market advances. The correction-aligned-calendar is the inverted phase of the same length that has lined up with major corrective lows.

Monthly observations from January 1928 through March 1989 were used to compare those two calendars. The inverted calendar lined up with major lows in years including 1929, 1932, 1937, 1946, 1962, 1970, 1979, and 1987.

Scale the oscillator to the dominant cycle

The same dominant-cycle length used to date anniversary windows can also scale the lookbacks of a cycle-tuned-oscillator. That line is the difference of two exponential moving averages whose periods are fixed fractions of the measured cycle. One construction uses one-quarter and one-half the cycle. Another uses one-sixth and one-third.

Oscillator troughs and crests serve as directional marks, and a further average of that oscillator is used as a trailing confirmation line.

A crest where a low had been expected

On monthly index data from 1975 through 31 March 1989, a 41-month-tuned oscillator and its confirmation line were cresting rather than troughing near a date previously treated as an ideal 40.68-month low. That pattern is consistent with a shift toward the inverted calendar.

Several 41-month alignments can coexist. One alignment that had marked highs in 1977, 1980, and 1983 later coincided with a 1987 low, showing a mid-history phase change inside the same cycle length.

An Elliott-wave Fibonacci check of the crash swing

Near the end of March 1989, price had not moved materially above a 61.8 percent Elliott-wave retracement of the decline from the August 1987 high to the December 1987 low. Breadth and momentum were described as weak. Those conditions supported the reading that the window was forming a high rather than a low.

That overlay is the elliott-wave-fibonacci-check. It maps a 61.8 percent retracement of a completed wave swing to test whether a cycle window is more likely a high or a low.

What would restore the original calendar

If the inverted calendar remains the better match, later significant lows were expected along that inverted sequence rather than on the original advance-aligned dates. A later failure of the inverted sequence to capture the most significant low would be read as a return to the original calendar.