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CyclepediaThe trading encyclopedia
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James Marsden Hurst 1924—2005
Chapter 2.4 — Timing Is the Key

Constant-width curvilinear envelope

Hurst's graphical band uses approximately constant, minimally sufficient width to estimate cyclic components; its latest section remains provisional.

On this page

Who this entry is for — Readers who need to distinguish Hurst's graphical envelope from a band calculated automatically around a moving average.

Primary source: J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970, pp. 37–38 and 69–74.

Definition

In plain terms — Sketch two curves around price, measure the distance between them and adjust them until the band is nearly constant in width and as narrow as possible without excluding non-isolated movements.

Hurst's curvilinear envelope is a graphical band formed by two bounds that follow price movement. The procedure seeks a compromise among:

  • constant width along the chart;
  • coverage of the great majority of the data;
  • the minimum width compatible with that coverage.

In Chapter 4, Hurst starts from a visual sketch, measures vertical thickness at several points and corrects the bounds. He allows two or three brief, isolated overruns when including them would require a considerable widening of the band. It is therefore inaccurate to describe the band as a judgment-free construction or as a mathematically unique container for every observation.

The constant-width envelope Synthetic series · illustrative centre guide, bounds at fixed distance. Price gallops between the bounds — and every contact is information. HURST 1970 · CH. 2 The constant-width envelope Synthetic series · illustrative centre guide, bounds at fixed distance CYCLEPEDIA DIAGRAM — EMICICLO wk 0 wk 26 wk 52 wk 78 wk 104 wk 130 wk 156 wk 182 wk 208 centre line A B C D E F G H I J LOW-TO-LOW SPANS 9 AVERAGE DURATION 20.4 weeks REFERENCE NOMINAL 26 weeks Price gallops between the bounds — and every contact is information.
Cyclepedia diagram: the bounds follow the observed component while maintaining an approximately constant distance; contacts help identify candidate extrema for measurement.
Select the highlighted points to explore the detail

What is measured

In plain terms — Contacts or near contacts with the bounds provide candidate highs and lows for the component the band is intended to isolate. Distances between troughs become wavelength samples.

Within Hurst's model:

  1. extrema associated with contacts with the band are marked;
  2. low-to-low or high-to-high distances are measured;
  3. variation and anomalous cases are examined;
  4. the observed mean is compared with the nominal-cycle scale.

Chapter 2 applies the procedure to the weekly Dow Jones Industrial Average from 1965 to 1969 and obtains seven selected samples with a mean of 21.428 weeks. That result belongs to the sample and selection described in the book; it is not a periodicity guaranteed for other markets or periods.

Limit — Excluding observations changes the estimate. A replication should document the points used, the points excluded and the exclusion criterion; a nominal label does not replace measurement.

Graphical bounds, centre line and moving average

The graphical centre line is the midpoint between the two drawn bounds. In the author's model, it is interpreted as the effect of longer components and of factors not isolated by the band.

A centred moving average can be used in mathematical implementations to construct or approximate a channel, but it is not automatically equivalent to the manual procedure on pp. 69–74. The method, span, edge treatment and width rule must be declared.

Example — “Hurst graphical envelope, width measured in ten sections” and “20-bar centred average ± fixed deviation” are different constructions. They may produce similar bands, but their definitions are not interchangeable.

Nesting

In plain terms — One band represents one scale. Drawing a wider band around the first, or examining the oscillations inside it, is used to look for longer and shorter components.

Nesting extends the procedure:

  • nesting up: a second envelope around the first for a longer component;
  • nesting down: analysis of internal oscillations for shorter components.

The hierarchy is a model hypothesis that must be compared with the data. Ratios close to two or three do not make every oscillation part of the same cyclic system.

Latest section and validity over time

The historical part of the envelope stabilises once well-defined extrema have been identified. The section near the latest observation remains estimated and can change as new bars arrive. Hurst indicates a maximum uncertainty on the order of half a cycle for the graphical method and updates the band after every new extreme.

Typical error — Drawing the final bound today with knowledge of future data and then presenting it as a signal that was available in real time. Validation must preserve the versions of the band that were actually observable at each date.

Summary card

  • Construction: sketch, measurement, correction and a coverage-width compromise.
  • Use: estimate extrema and wavelength within the Hurst model.
  • It is not: necessarily a moving average or a unique band.
  • Real time: the latest section is provisional.

Sources

  • J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970, pp. 37–38 — introduction of the envelope and measurement of the component on the DJIA.
  • J. M. Hurst, same work, pp. 69–74 — graphical procedure, minimum width, observations outside the band and validity of the latest section.
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