James Marsden Hurst 1924—2005

Chapter 2.4 Timing Is the Key

Constant-width curvilinear envelope

A band of uniform vertical thickness enclosing prices; the starting point of Hurst's observational cyclic analysis.

On this page

Who this entry is for — The first thing drawn on a Hurst chart: a curved band wrapping the prices. From there, cycles are measured. Without the envelope, observational analysis does not start.

Source: J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970 — Chapter 2 (pp. 37–38); construction mechanics in Chapter 4.


Prerequisites

Five principles of the cyclic model — why price oscillates. Here: how the oscillation is made visible.


Definition

In plain words — Two curved lines, above and below price, with the same vertical thickness for the whole period. Not drawn by eye: they follow fixed rules.

An envelope is a curvilinear band around a high-low chart meeting three conditions:

  • it encloses all the data — in the book's sample (DJIA 1965–69) the only tolerated exception is the peak of a single week in May 1968;
  • it has constant vertical thickness, "uniformly and precisely" identical over the whole time span;
  • it is unique, built according to fixed rules (the step-by-step mechanics belong to Chapter 4).

It is always — the book's words — "the starting point for observational cyclic analysis".

HURST 1970 · CH. 2 The constant-width envelope Synthetic series with true variation · centre = 21-bar centred average, 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.
The envelope actually computed on a synthetic series with true variation: bounds at fixed distance from the centred average, letters at the lower contacts, dashed centre line.
Tap the letters, the centre line and the bound
Fig. II-3 — constant-width envelope on the weekly DJIA
The original 1970 plate: Fig. II-3, the envelope on the weekly DJIA 1965–1969.

What the contacts say

In plain words — When price touches the lower or upper bound, you are looking at a low or a high of the dominant cycle. Count the weeks between two lows → you measure the cycle's current duration.

Price "gallops back and forth" inside the band, and the points of contact (or near contact) with the bounds are highs and lows of the cyclic component the envelope isolates. From there, the book's exercise: letters on the lows, counting the weeks, discarding the variants, averaging — on the DJIA 1965–69 the result is 21.4 ± 3.5 weeks, the current expression of the 26-week nominal (the full measurement, row by row, is in Hurst nominal cycles).

Lows, Hurst warns, are better defined than highs: always count from the lows.


The centre line

In plain words — The line midway between the two bounds is a gift: it shows everything slower than the cycle you are watching — trend included.

Drawing a line midway between the bounds yields the representation of the sum of all cyclic components of longer duration than the observed one, plus the fundamental trends in force (p. 38). It is information the operating chapters will use constantly: the cycle you watch rides the centre line, and the centre line tells you where everything else is going.

Example — Low on the lower bound at week 10, next low at week 33: 23 weeks → the 26-week nominal row, deviation −3, inside the book's range. Meanwhile the centre line is rising: the cycle is working inside a favourable current.


Limits

Warning — The envelope is a photograph of the past: its centre (a centred average) stops by construction half a cycle before the last data point. How to extend it in real time — and what that costs — is Chapter 4 material, not this entry's.


Summary card

Element Meaning
Upper bound Highs of the observed cycle
Lower bound Lows of the observed cycle (the reliable ones to count)
Centre line Trend + all slower components
Constant thickness A construction rule — not an aesthetic parameter
Allowed exceptions Isolated spikes (in the book: one week in four years)