11.1 Foundations of Cycle Theory

Cycle analysis sits inside Classical Techniques, which carries 33% of CMT Level I—the 132-question, 2-hour sitting (120 scored plus 12 unscored pilots). The 2026 Program Guide lists cycles as Section Eight: Cycle Analysis, immediately after Sentiment. This OpenExamPrep section is independent study material for foundations of cycle theory: the two cycle families Level I actually uses, the three numbers that define a wave, J.M. Hurst's Principles of Commonality, harmonics, the composite wave, left versus right translation, the dominant cycle, and the identification tools (visual trough counting, detrending, and a centered moving average). Independent CMT Level I practice by OpenExamPrep is at /practice/cmt.

A cycle is a recognizable event—usually a price trough (low) or crest (high)—that repeats with a measurable rhythm. Cycle theory asserts that long and short cyclical forces help drive price. You are not asked to publish a dated forecast of the next low. You are asked to name the parts, read a composite, and tell translation from a sketch.

Two types of cycles Level I wants you to name

CMT learning objectives ask you to name the two types of cycles. For this exam, the useful pair is time cycles versus seasonal/calendar cycles. A related third family, harmonic price-time cycles, shows up as vocabulary, not as a full squares-of-price-and-time course.

Time cycles have a period measured on the clock or in bars: 20 weeks, 40 days, 4 years. Hurst's nested waves live here. You count trough to trough (low to low) unless a stem explicitly uses crest to crest. The period can drift (see variation below), but the object is still a time-length oscillation.

Seasonal/calendar cycles are tied to the diary: month of the year, day of the week, tax dates, harvest windows, year-end rebalancing. The period is calendar-fixed (the year always has twelve months). Amplitude and phase still matter: how large is the typical seasonal swing, and in which month does the typical high or low fall? Section 11.2 puts names on economic and seasonal examples. This section only needs the type.

Harmonic price-time cycles treat a measured swing as a unit that can be copied in price and in time by small integer ratios (halves, doubles, sometimes thirds). They are not the same as a 12-month seasonal. If a stem says "harmonic cycle," think ratio of a completed range, not "January effect."

Some CMT notes also split fixed (linear) cycles from non-fixed (nonlinear) sequences. Time and seasonal cycles are the linear family: a roughly constant period. Fibonacci time counts and 3-wave/5-wave sequence language (11.2) are nonlinear: the intervals are not one repeating length.

Three defining characteristics: amplitude, period, phase

Every cycle you can draw as a wave has three numbers.

Period (wavelength) is the time from trough to trough (or crest to crest). A 20-week cycle that bottoms in week 0, week 20, and week 41 is still "about 20 weeks" under variation.

Amplitude is the height of the wave: crest minus trough in price, or in residual units after a detrend. Longer cycles tend to have larger amplitude (proportionality).

Phase is where you are inside the period. If the last trough was 5 weeks ago and the period is 20 weeks, you are a quarter of the way through the cycle, typically heading toward the crest if the wave is still right-translated. Phase is the characteristic you use when comparing two cycles of different lengths that may trough together.

Worked numbers: a residual oscillates from −8 to +8 over 16 bars. Peak-to-trough height is 16; some stems call amplitude the half-range of 8—read the wording. Period is 16 bars trough-to-trough. If today's residual is 0 and rising after a trough four bars ago, phase is about 4/16 of the way from the low.

Exam trap: treating volume as a fourth defining characteristic of the cycle object. Volume can confirm a turn. The cycle's three parameters remain amplitude, period, and phase.

Hurst's Principles of Commonality

J.M. Hurst, in The Profit Magic of Stock Transaction Timing and his later cyclic course, described how market waves behave. The CMT Level I objective is to list and define Hurst's seven Principles of Commonality. This OpenExamPrep section uses these seven names: commonality, harmonicity, summation, synchronicity, proportionality, nominality, and variation.

Hurst's fuller cyclic theory is often restated as eight principles by adding cyclicality: price movements are combinations of waves and therefore look cyclic. That idea already sits inside summation and inside the definition of a cycle. If a stem asks for seven Principles of Commonality, use the seven names below. If a Hurst excerpt lists eight, cyclicality is the extra name—this guide will not invent a different seventh label.

Harmonics are those integer-ratio companions. If the dominant cycle is 20 weeks, the second harmonic is about 10 weeks, and the next doubling is about 40 weeks. You look for nested troughs: the 10-week lows sitting inside the 20-week rhythm. Harmonicity is why cycle work talks in octaves instead of a junk drawer of unrelated lengths.

Composite wave, translation, and the dominant cycle

The composite wave is the summation result: what you actually see on the chart after the components add. Imagine a 20-week wave of amplitude 10 and a 10-week wave of amplitude 5, both starting at a common trough. When both are down, the composite makes a deep low. Near the longer wave's theoretical crest, the shorter wave can be down, printing a mid-cycle dip. The visible high is therefore not exactly at the longer wave's sine-wave peak. That is why cycle crests look messier than cycle troughs, and why synchronicity is stated for lows, not for highs.

Translation is where the crest sits between two troughs.

• Draw troughs at week 0 and week 20. Midpoint = week 10.
• Left translation: crest before the midpoint (example: week 7). The market spent more time falling. Typical of a downtrend.
• Right translation: crest after the midpoint (example: week 13). The market spent more time rising. Typical of an uptrend.
• A crest at the midpoint is a symmetric cycle: no translation.

Translation is a trend check, not a new oscillator. If a formerly right-translated wave starts printing left-translated crests, the uptrend is aging. Do not reverse the names: "left" means the peak is left of center (early), not "beyond the halfway point."

The dominant cycle is the component that currently does the most work on price: usually the largest-amplitude wave that remains visible after you quiet shorter noise. Dominance can pass from one length to another. Naming the dominant cycle is an identification claim, not a promise that next week's low will print on a forecast date.

Tools that aid identification

1. Visual trough counting. Mark successive meaningful lows. Measure the intervals. If lows fall at session 10, 31, 52, and 74, the gaps are 21, 21, and 22—a candidate ~21-bar period. Ignore one-bar spikes. Count low to low.

2. Detrend. A rising market hides oscillations. Two teaching methods: subtract a moving average (or a fitted trend line) from price so the residual oscillates around zero; or express price as a percent distance from that average. Troughs in the residual are easier to count than troughs that keep stair-stepping up.

3. Centered moving average. An ordinary SMA lags. A centered MA of length n is plotted at the middle of its window (about (n−1)/2 bars back). It sits through the middle of the oscillation instead of trailing it. Because centering uses future bars, the last (n−1)/2 points are incomplete—this is an identification and research tool, not a live trigger.

Worked detrend: price 50, 52, 51, 54, 58 riding a 5-bar SMA that itself is rising 51 → 54. Residuals might print −1, 0, −2, +1, +3. The residual's low is the cycle trough you wanted, without the uptrend stealing the picture.

On the exam, walk this order: name the cycle type, read amplitude / period / phase, apply the Hurst principle the stem is testing, locate the crest for translation, and say which tool would reveal the dominant wave.

Key Takeaways

• Two useful types: time cycles and seasonal/calendar cycles; harmonic price-time cycles are a related ratio family
• Three characteristics: amplitude, period, phase
• Seven Principles of Commonality as named above; cyclicality is the extra eighth name in many Hurst restatements
• Composite wave = summation; left translation = early crest (downtrend); right translation = late crest (uptrend)
• Identify with trough counts, detrends, and centered moving averages