Who this entry is for — A moving average smooths by throwing the short waves away. The book's question: is there useful information in what it throws away? Answer: exactly the cycle you needed — the trailing-level one — with its magnitude served on a plate.
Source: J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970 — Chapter 6, Now Turn Your Moving Averages Inside Out → Try the Inverse Average in Other Ways (pp. 109–112, Fig. VI-8).
Definition
In plain words — Subtract the average from the price (aligned properly: half a span back!). The average held only the long cycles; the difference holds only the short ones. Plot it as bars from a zero line: the hidden cycle appears.
An average of span N reduces the N-duration component to zero and keeps only the longer ones. Subtracting the average from price removes all those long ones: what remains is what the average had "thrown away" — the components shorter than N. The one critical item, "as always", is matching average and price points properly, accounting for the half-span lag before subtracting. With an odd span every average value has its own bar: direct subtraction, no interpolation.
What it reveals (on Alloys)
Applied as the inverse of the half-span (11 weeks, odd, on Alloys Unlimited), the subtraction reveals three things at once:
- the component next shorter than the trading cycle, finally sharp: nominal duration 12.7 weeks (spread 10–16) — precisely the cycle on which trailing levels are built;
- magnitude read directly: 7 points peak-to-peak (±3½) — "without necessity for, and without the error inherent in, the construction of envelopes";
- all of it for free: the half-span was already computed anyway.
And the operational proof: short opened at 51–52, prices "refusing to go down" for nine weeks. The inverse says: the 12.7-week cycle is 7 weeks along → next low in 3–9; the 21.7-week trading cycle (20–23) is 19 along → low in 1–4. Both due: more downside ahead. The residual-magnitude sum: 6/13 of 7 points ≈ 3.7 from the short cycle, plus 3/22 of 14 ≈ 1.9 from the trading cycle → ~4.6 points from 45 = 40½. The half-span alone had said 40⅝ — "almost identically, yet obtained using information the half-span average threw away". The stock bottomed at 41 the next week.
The other uses
Card — When to pull it out
- Inspecting any component: span = the component's duration → it appears at exact magnitude on a zero baseline.
- Near buy/sell points: extracting the fast components removes all doubt about trend-line validity and channel turns.
- Before a buy: extract the trading cycle — if magnitude fluctuation has shrunk it to near zero, the valid signal will not pay.
- On triangles: the formation mechanics (short components' fluctuation) become visible, and resolution times sharpen.
Warning — Components just longer than the span do not pass through the average "unscathed": near the cutoff the attenuation is strong (the exact mathematics is in Appendix IV). The inverse therefore also carries a residue of the middle cycles: you read the dominant component — you do not expect spectral surgery. For that, there is Chapter 11.
Summary card
| Element | Rule |
|---|---|
| Formula | Price − centred average (aligned −½ span) |
| Content | Only components shorter than the span (+ residues near the cutoff) |
| Recommended span | Odd; = half-span for the trailing cycle |
| Magnitude | Read directly on the zero baseline, no envelopes |
| Uses | Trailing, target confirmation, pre-buy check, triangles |
Links
- Half-span and full-span — the average it is born from
- Case Alloys Unlimited — the 40½ confirmation
- Computational methods — Chapter 6's framework
- Hurst tradition — chapter index