Function klinger

Klinger Volume Oscillator (Stephen Klinger, 1997) — the difference of two EMAs of a volume force that carries its own trend state. Kernel K6 feeding the K2 engine.

trend[i] = (high+low+close)[i] > (high+low+close)[i−1] ? +1 : −1
dm[i]    = high[i] − low[i]
cm[i]    = trend[i] === trend[i−1] ? cm[i−1] + dm[i] : dm[i−1] + dm[i]
vf[i]    = volume[i] × |2 × (dm[i]/cm[i] − 1)| × trend[i] × 100

${prefix}       = EMA(vf, fastPeriod) − EMA(vf, slowPeriod)
${prefix}Signal = EMA(${prefix}, signalPeriod)
Copy

Appends two columns (kvo / kvoSignal at the default prefix). Reads four — high, low, close and volume — each named by an option defaulting to its DEFAULT_OHLCV name.

Which Klinger — F-AMBIG, and the fork is named

The corpus assessment flags this study F-AMBIG and it earns it: two different formulas ship under the name.

• This study is the original, as Klinger published it and as StockCharts documents it: the volume force above, with the trend state and the cumulative measurement. The |2 × (dm/cm − 1)| factor is the part every restatement garbles; the reading taken here is 2 × ((dm/cm) − 1) under the absolute value, not 2 × (dm/cm) − 1. The two differ by a constant inside the modulus and therefore by a different amount on every bar; the oracle carries a case that separates them.
• The named alternative is TradingView's ta.kvo, which drops the dm/cm factor entirely: its volume force is just ±volume × 100 on the sign of the HLC change, so it is an EMA-pair oscillator of signed volume and no state machine at all. It is not implemented here, and it is not an option on this study — the two are different indicators that share a name, and a variant knob would hide that. Measured on the oracle's 80 bars, the two disagree by more than the oscillator's own range: the simplified form's kvo spans a different order of magnitude entirely (the generator prints both).

The EMAs are pond's — first-sample seed, α = 2/(span+1), the movingAverageValues array door — matching macd and for the same reason (making them TA-Lib-seeded here would make this study's EMAs disagree with ema() inside the package). TA-Lib has no Klinger, so nothing arbitrates it.

Warm-up — per column

The volume force starts at bar 1 (it needs a predecessor for the trend comparison and for dm[i−1]), so on gap-free input the oscillator starts at bar slowPeriod and the signal at slowPeriod + signalPeriod − 1. Each column is emitted where it is genuinely defined rather than both waiting for the slower — the same per-column warm-up macd uses.

Edges

• Scale behaviour is mixed, and the mixture is the point. The volume force is volume × (a ratio of ranges) × ±1 × 100, so the study is linear in volume (double every volume and both columns double) but invariant to a price scale and a price shift: dm/cm is a ratio of ranges, so a scale cancels and a shift never reaches it, and the trend flag compares two high + low + close sums, which a positive scale and a +3c on both sides both preserve. Adding a constant to every volume is not a no-op, unlike negativeVolumeIndex, which only compares volumes — the force multiplies by one. All four are asserted as property tests.
• A zero-range leg (cm = 0, which needs every bar in the leg to have high === low) is a genuine 0/0 and reads undefined for that bar; the EMAs then propagate it, since a recursion has no state to carry across a hole. There is no guard for it: cm is a sum of non-negative ranges, so a zero cm forces a zero dm with it and the ratio is NaN on its own — a guard would be dead code.
• A missing cell in any of the four inputs resets the K6 machine ([PND-SFOLD]): the volume force is undefined for that bar and the trend/cm state re-seeds from the next complete pair. The EMAs downstream nonetheless carry the undefined forward — pond's EMA skips a missing bar in its recursion, so the oscillator resumes, but the two spans resume at different points, which is why an interior gap is best filled before running this.