Function priceVolumeTrend

Price-Volume Trend — a running total of each bar's volume scaled by its fractional price change:

PVT[i] = PVT[i−1] + volume[i] · (close[i] − close[i−1]) / close[i−1]
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The third member of the cumulative-volume family, between obv and accumulationDistribution in how much of a bar's volume it counts: OBV takes the whole of it on the sign of the close change, A/D grades it by where the bar closed in its range, and PVT scales it by how far price moved. A 3% up-bar therefore contributes three times what a 1% one does, where OBV would count them the same. As with both, the level is arbitrary and the slope is what is read.

No period — there is nothing to size a window over.

The fraction, not the percent

The rate of change comes from percentChangeValues, which is pond's percentChange / TA-Lib's ROC and therefore returns a percent (×100). PVT's published definition is the fraction, so the study divides by 100 rather than re-deriving the ratio: one definition of "price change", shared with the study TA-Lib validates, and a constant that is visible in one place. (The two conventions differ by a factor of 100 in the level, which matters only when comparing against another package's PVT.)

The first bar has no value

PVT[0] is undefined, not 0. ChartIQ's definition (and every other published one) is a recursion on the previous close, so bar 0 has no term — and unlike obv, whose volume[0] seed is TA-Lib's convention and is matched for exactness, PVT has no TA-Lib function and so no convention to defer to. Seeding at 0 would print a level for a bar whose term could not be computed; every later level is identical either way (the seed-at-zero line is this one with a 0 painted on bar 0), so nothing is lost by declining to invent it. This is also just what the composition gives: the leading NaN shifts cumulativeValues' seed.

Definition, verified

TA-Lib has no PVT, so the oracle is a pandas replication — (pct_change · volume).cumsum() — with the analytic first valid bar (1) asserted, and separated from the obv shape on the same input so a study that dropped the magnitude could not pass.

Edges

• A leading gap in either input shifts the seed to the first bar with a defined term (bar 1 on clean input), so PVT over another study's output starts at that study's first value rather than coming back empty.
• An interior gap propagates to the end — the running-sum rule (cumulativeValues). A missing close costs two terms (its own bar and the next, which reads it as the base), which is moot once the sum has gone.
• A zero previous close → no term, so the line stops there. That is percentChangeValues' guard: x / 0 is ±Infinity, which is not a rate of change. Only reachable on a column that can be zero (a redirected close); real prices are positive.
• Linear in volume; invariant under scaling every price (the fractional change is scale-free), but not under shifting them — a shift changes the base of every ratio. Pinned by property tests.