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.
On p. 37, Hurst presents the envelope as unique and exactly constant in vertical thickness. This is the author's description of his ideal channel. The procedure on pp. 69 and 74 nevertheless requires sketching, measuring and correcting by hand: constant width is the criterion to pursue, while its graphical execution remains approximate.
The vertical distance between the bounds is measured at several points, an average is chosen and the band is corrected. Wider and narrower constructions are then compared. Hurst allows two or three isolated observations outside the band when including them would require considerable widening. The title therefore retains the historical name; it does not imply that a judgment-free algorithm produces a single possible container for every observation.
What is measured
Contacts or near contacts with the bounds provide candidate highs and lows for the component the band is intended to isolate. Distances between lows become samples of cycle duration (wavelength).
Within Hurst's model:
- extrema associated with contacts with the band are marked;
- low-to-low or high-to-high distances are measured;
- variation and anomalous cases are examined;
- 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.
Measurement example — At two sections of a chart with a linear price axis, the bounds are 112 and 88, then 117 and 93. Both widths are 24: the band's level changes, its thickness does not. Measure vertically at the same date, not along a perpendicular to a curve. This is a teaching example, not prices from the book.
Nesting
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
On p. 71, Hurst treats the section preceding the latest well-defined high or low as settled. He calls the time elapsed since that extreme the channel's validity lag and limits it to half a cycle within his model's reasoning. This is not a measurement of maximum price error or a statistical confidence interval.
The section near the latest observation remains estimated: the author instructs readers to draw it lightly and change it as new bars require. The historical claim that the preceding section will never change again depends on having identified the extrema correctly. A retrospective reconstruction does not show that they could have been recognised in the same way in real time.
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, p. 69 — construction and vertical measurement; p. 71 — estimated section and validity lag; p. 74, Fig. IV-2 — compromise between width and observations outside the band.