Immediate definition
In plain terms — An inverse moving average is the distance between price and a centred moving average. Remove the slow line and a fluctuation around zero remains, making shorter movements easier to see.
The name does not mean an average calculated “backwards.” It is a residual: what remains after a smoothed, correctly aligned version of the same series is subtracted from price. A positive value means price is above that slow line; a negative value means it is below. On its own, it does not say where the next bar will go.
How to build and read it
If P_t is price at time t and C_t is the centred average, the
inverse is I_t = P_t − C_t. First calculate the average over the chosen
span—the number of bars in the window—assign each result to its centre, and
only then subtract. Hurst preferred odd spans because the centre lands on an
actual bar.
The distance between comparable troughs suggests the observed duration of the dominant component in the residual. The vertical distance from peak to trough measures its range in price units. Both are sample estimates: noise, nearby components and regime changes can shift them.
The operational limit: the edge
For an odd span N = 2k + 1, the centred average at time t needs k
observations before and k after that point. At the latest date, therefore,
the last k centred averages are unavailable, as are the corresponding
inverse values. This is more than a cosmetic chart lag: the required future
observations do not yet exist.
Software may leave the edge blank or estimate it with a projection or causal filter. An estimated edge is not the same quantity as the observed historical section and may change as new bars arrive. A trader should therefore check how the platform handles endpoints before treating the line as live. No edge method turns the inverse into a certain entry, exit or target confirmation.
Technical precision and attribution
The use described here belongs to J. M. Hurst's 1970 method; it is not the Hurst exponent used to study long-range dependence. In the Chapter 6 Alloys Unlimited example, Hurst subtracts an 11-week centred average, reads an estimated 12.7-week component in the residual, with an observed 10–16-week spread, and measures a peak-to-peak range of about seven points. He uses this evidence alongside other parts of the method as historical confirmation, not as a standalone oracle.
In filter terms, the subtraction is the moving average's high-pass complement: it attenuates slower movement and retains more of the faster movement. The cutoff is not sharp. A moving average's response leaves attenuated components and residual side lobes; Hurst's Appendix IV reports errors reaching roughly 23% in parts of that response. A selected span does not perfectly isolate a single cycle.
Sources
- J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970, Chapter 6, pp. 109–113 and Appendix IV, pp. 210–211 — construction, Alloys Unlimited example and filter response.
- OCLC WorldCat, The Profit Magic of Stock Transaction Timing — bibliographic record — authorship, publisher and first-edition date.
- NIST/SEMATECH, Centered Moving Average — window centring and the distinct treatment required for even orders.
- Rob J. Hyndman and George Athanasopoulos, Moving averages — Forecasting: Principles and Practice — symmetric formula and missing endpoint estimates.
Links
- Moving average — the general concept before the historical variant.
- Hurst cyclic moving averages — span, centring and filter response.
- Hurst computational methods — the inverse's role in Chapter 6.
- Alloys Unlimited case — the full context of the example.