Williams' Accumulation/Distribution (no volume) (WAD)

Summary

Williams' Accumulation/Distribution: a cumulative line that measures each bar's close against the true range extreme — the previous close, whenever it lies outside the current bar — rather than against the bar's own high and low. A close above the previous one accumulates the distance up from the true low; a close below it distributes the distance down from the true high; an unchanged close contributes nothing.

It consumes no volume. Larry Williams' original multiplies each move by that bar's volume; Steven Achelis published the modification that drops the multiplier (Technical Analysis from A to Z, 2nd ed., p.368), the industry kept Williams' name on it, and that no-volume form is what Tulip Indicators and pandas-ta-classic ship — so it is what TA-Lib ships under this name. The volume-weighted original is a different series. WAD is grouped with the volume indicators for discoverability next to AD, ADOSC and OBV, not because it reads volume.

Formula

TRH_t = max(close_{t-1}, high_t); TRL_t = min(close_{t-1}, low_t); AD_t = close_t - TRL_t if close_t > close_{t-1}, close_t - TRH_t if close_t < close_{t-1}, otherwise 0; WAD_t = WAD_{t-1} + AD_t

The first bar of the requested range has no previous close, so it contributes 0 and the line starts there — the same convention as AD, OBV, NVI and PVI. The accumulator restarts wherever the caller starts, so a different startIdx shifts the whole line by a constant.

Inputs

inHigh — High price of each bar
inLow — Low price of each bar
inClose — Close price of each bar

Outputs

outReal — Cumulative accumulation/distribution

Properties

Numerical Stability: Path-Dependent


☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: wad.c · wad.yaml

Native	File
C	`ta_WAD.c`
Rust	`wad.rs`
Java	`Core_WAD.java`
C#	`Core_WAD.cs`

TA-Lib is also available for Python, R and more using a wrapper.

References

Larry Williams is the originator; Steven Achelis, Technical Analysis from A to Z, 2nd edition, page 368 publishes the no-volume form this ships, with the worked 12-bar example pinned in the test suite.
IncredibleCharts, Williams Accumulation Distribution — Williams' volume-weighted original, AD = Price Move × Volume over the same true-range price move.
IncredibleCharts, Williams Accumulate Distribute — the Achelis form under its disambiguating name, "not a volume indicator despite the name".
Tulip Indicators ti_wad and pandas-ta-classic wad both compute this form; the two are external oracles for it, at a one-element alignment offset and index-for-index respectively.