Cyclic analysis: cycles, phases and timing

Cyclic analysis is a family of methods that looks for recurrences in price oscillations and estimates their duration, amplitude and phase. An observed recurrence can suggest a timing hypothesis; it does not prove that the movement will repeat or establish its probability.

In simple terms — If some lows recur at similar intervals, we can measure those intervals. To use the measurement for the future, we must check how the lows were selected and whether the relationship holds on subsequent data.

This entry introduces the general vocabulary and distinguishes the historical J. M. Hurst study path. His principles belong to a school’s model, not to a universal definition of cyclic analysis.

From measurement to hypothesis

Define the data: instrument, historical interval, price series and time unit. Fifteen daily bars are not necessarily fifteen calendar days.
State the method: how turning points are identified, which window is used and which transformations are applied. In spectral analysis, for example, NIST describes looking for recurring frequencies in regularly spaced observations and removing any trend.
Measure and update: estimate duration, amplitude and phase, recording exclusions and revisions. New data may change the earlier interpretation.
Test the forecast: formulate a rule before the test data and check it outside the sample used to select it. If a low needs later bars for confirmation, a decision can use it only after that confirmation.

Testing a probability in cyclic analysis

Three hypothetical intervals of 14, 16 and 15 bars have a mean of 15 bars. That mean describes the sample: it assigns no probability to the next low and does not justify a countdown. A forecast percentage requires a defined event and a comparison of predicted percentages with observed frequencies on data not used to construct it.

The spectral plot described by NIST is a general statistical tool: a peak within the sample does not, on its own, validate a market strategy. For operational testing → Backtest and Data leakage.

Core concepts

Concept	What is measured
Period / duration	Time between equivalent points of an oscillation, such as two lows attributed to the same component
Phase	Estimated position within the cycle relative to a stated origin
Amplitude	Vertical size of the oscillation; state whether measured from centre to crest or from trough to peak
Nesting	nesting envelope

These measurements depend on the method. A turning point visible in the combined price does not automatically identify the low of every hypothesised component.

What belongs to the Hurst school

Hurst proposes nominal reference durations and varying oscillations. In his 1974 article, synchronicity is the principle that component troughs coincide when their duration relationships allow it. This is a model hypothesis: alignment alone supplies no verified probability of a turn.

The price motion model and nominal cycles develop the historical formulation. Tools in this path include the curvilinear envelope, valid trend line (VTL) and FLD. VTLs are already described in the 1970 book (p. 78); the 1974 article mentions VTLs and FLDs as action signals and refers readers to the course.

Relationship to other disciplines

Discipline	Question to examine	Path
Cyclic analysis	Which timing recurrences emerge, and how stable are they?	Cyclic analysis
Price and volume	How does the quantity traded change relative to price movement?	Wyckoff tradition
Classical technical analysis	Which structures, patterns and indicators describe the movement?	Technical analysis

Aggregate volume alone does not identify who buys or sells. Combining cyclic and volume signals is a choice to test: it does not demonstrate an advantage over the individual signals or replace risk management.

Historical study path

Five principles of the Hurst cyclic model
Hurst nominal cycles
Chart pattern verification (Ch. 3)
After the book — post-1970 Hurst (FLD, phasing)

Sources

NIST/SEMATECH, e-Handbook of Statistical Methods, § 1.3.3.27, Spectral Plot — frequencies, regularly spaced sampling and trend; a general statistical reference.
J. M. Hurst, The Profit Magic of Stock Transaction Timing (1970), Ch. 2, pp. 32–41 and p. 78 — nominal model, chart measurements and VTLs; printed page numbers.
J. M. Hurst, “Cyclic Analysis”, Reason, May 1974, Wave Functions and Relationships in Price Movement and the passage on VTL/FLD — the school’s later formulation.