Skip to content
CyclepediaThe trading encyclopedia
ITENESPT-BRFRDE
James Marsden Hurst 1924—2005
Chapter 6.2 — Calculate Your Own Way

Hurst half-span and full-span averages: method and limits

Hurst's half-span and full-span averages compare a cycle with its channel centre; the procedure requires extrapolation and is not a standalone forecast.

On this page

Immediate definition

In plain words — Hurst uses two centred moving averages to read a cycle: the half-span covers half of its duration, while the full-span covers the whole duration and approximates the channel centre.

If the observed cycle's average duration is T, the two spans are T/2 and T. In the cyclic model Hurst published in 1970, a half-span reversal signals that the move attributed to that cycle is roughly halfway complete. This is a rule within that historical model, not a universal property of prices.

Why a `T/4` delay appears

A centred moving average is assigned to the middle of its window. The half-span has a window of length T/2, so its latest complete value lies half a span before the last bar: (T/2)/2 = T/4. With a 20-week cycle, for example, the 10-week average has an operational delay of 5 weeks.

Hurst interprets that quarter-cycle as the stretch between one extreme and the midpoint of the next swing. Therefore, when the 10-week average displays a reversal, price has already completed about half of the leg associated with the 20-week cycle in his model.

The 1970 procedure

The sequence described in Chapter 6 is short:

  1. estimate T through cyclic and envelope analysis;
  2. calculate centred averages with spans T/2 and T;
  3. when the half-span reverses, extend both curves graphically through the still-missing right-edge segment;
  4. identify level C, where price and the extrapolations meet.

For an upward leg, if the previous low is L, the distance already travelled is d = C − L, and the historical target is C + d. For a downward leg, start from the preceding high and subtract the same distance. Hurst places a band equal to ±10% of the estimated total move around the result. It is a practical tolerance in his procedure, not a statistical confidence interval.

Half-span and full-span in Hurst's historical method Observed price, half-span average of length T divided by two and lag T divided by four, full-span average as theoretical channel centre, and an uncertain extrapolated right edge. HURST 1970 · CHAPTER 6 Half-span, full-span and the unobserved edge Historical geometric relationships, not a guaranteed outcome observed pricehalf-span T/2full-span Testimate, not data observed sectionunobserved edge half-span = T/2 lag ≈ T/4 Half-span T/2: half a cycle, not a deterministic signal Full-span: theoretical centre with possible residuals Edge: recent centred values cannot yet be observed Extrapolation: an estimate subject to uncertainty Tab or tap: explore the four points
The half-span supplies the reversal point; the full-span approximates the channel centre. The crossing and band depend on extrapolated, not yet observed, segments.
Select the highlighted points to explore the detail

The full-span and the channel centre

An average with span T theoretically cancels a component whose duration is exactly T. In Hurst's additive model, what remains is mainly the slower components, interpreted as the centre line of that cycle's channel. Shorter components do not all disappear: some may leak through and require graphical smoothing.

The full-span can also help in drawing the envelope. In the historical Alloys Unlimited case, its slope suggested a channel turn before the envelope alone could confirm it. Hurst nevertheless advises revising T and rebuilding both averages when the resulting channel yields a different duration estimate.

Right edge, time and uncertainty

The two lines do not actually reach the latest bar: the half-span is missing T/4, and the full-span is missing T/2. The method's final segment is thus an extrapolation, not an observed value. It can change as new bars arrive or when another curve is chosen; a chart that draws it without distinction hides the main operational limit.

Hurst adds a time estimate: the expected extreme lies about T/4 after the date of the extrapolated crossing. His own examples show a broad spread. With 5 weeks predicted, one case took 9 weeks; others entered the band after 3 and completed the extreme between 5 and 6 weeks. Envelopes, valid trendlines, price signals and risk defences therefore remain necessary. The half-span, full-span, ±10% band and T/4 timing are not a standalone forecast or a guarantee for an individual trade.

The source-checked label on this entry confirms correspondence with Hurst's text; it does not constitute contemporary empirical validation of the method.

Sources

Suggest an edit My proposals