Cumulative Sum (CUMSUM)

Summary

Cumulative Sum: the running total of a series from the anchor bar forward. A math primitive rather than an indicator — it is the one operation between the shipped corpus and three named classical breadth indicators: the A/D Line is CUMSUM(SUB(advances, declines)), the A/D Volume Line is CUMSUM(SUB(advancingVolume, decliningVolume)), and the McClellan Summation Index is CUMSUM of the McClellan Oscillator.

SUM is a rolling window over optInTimePeriod bars; CUMSUM has no window — every bar since the anchor contributes.

Formula

out[j] = inReal[startIdx] + inReal[startIdx+1] + … + inReal[startIdx+j]

Left-to-right in one double, no compensation — the same plain += convention the shipped accumulators (AD, OBV) use.

The accumulator re-seeds at the anchor. CUMSUM(3, 7, x) starts its total at x[3]; it does not warm up from x[0]. This is the published contract of the indicators built on it (StockCharts: only the A/D Line's shape carries meaning, the first value is "simply Net Advances for one period") and the convention of every shipped path-dependent function. The path_dependent flag declares exactly this class.

Inputs

• inReal — Source series (canonically a per-bar net figure, e.g. advances − declines)

Outputs

• outReal — Running total since the anchor bar

Notes

• Lookback 0: outBegIdx = startIdx, one output per input bar. Streaming state is a single accumulator, so a peek commits nothing by construction.
• The sum is uncompensated. A Kahan or Neumaier variant would diverge from AD's own convention, which this follows.

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: cumsum.c · cumsum.yaml

Native	File
C	ta_CUMSUM.c
Rust	cumsum.rs
Java	Core_CUMSUM.java

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