Function priceMomentumOscillator

Price Momentum Oscillator (Carl Swenlin, DecisionPoint) — a one-bar percent rate of change put through two stages of DecisionPoint's custom smoothing, scaled by ten, with a span-EMA signal line:

roc             = 100 · (price[i]/price[i−1] − 1)
stage₁          = customEMA(roc, 35)          α = 2/35
${prefix}       = customEMA(10 · stage₁, 20)  α = 2/20
${prefix}Signal = EMA(${prefix}, 10)          α = 2/11
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Appends two columns. Double-smoothing a one-bar rate of change is what makes this readable at all — the raw series is noise — and the result is a slow momentum line read on zero crossings and on crosses of its own signal.

The line is named ${prefix}, not ${prefix}Line — the trix shape, with the signal keeping the family suffix.

"Custom smoothing" is α = 2/n, and it is NOT the K2 engine's ema

This is the one definition in the package that is not a span EMA. DecisionPoint defines its smoothing multiplier as 2/n where every other EMA in this package (and in TA-Lib, and in pandas' ewm(span=n)) uses 2/(n+1). At n = 20 that is 0.1 against 0.0952 — a different rate, not a different seed, so it cannot be expressed as a span and rounding it to one would ship a differently-named indicator.

Measured on the oracle input: building both stages on the span EMA instead puts the line 0.106 away on a reading whose scale is 3.906 — about 2.7%, which is visible on a chart and invisible in a spot check. So the study composes on alphaEmaValues, the kernel door that takes α directly. That door exists only for this study; every other consumer takes a span, because a span is the vocabulary the whole package and every vendor speaks.

The signal line is a plain span EMA (α = 2/11), not a custom-smoothed one — DecisionPoint specifies "a 10-period EMA of the PMO Line", and the asymmetry is theirs rather than an oversight here. Measured, a custom-smoothed signal would sit 0.088 away, the same order as the stage difference above, so this is stated rather than left to chance.

Where the ×10 goes — nowhere, measurably

DecisionPoint writes the scaling between the two stages (customEMA(10 × stage₁, 20)) and that is what the code does, but every stage is homogeneous, so multiplying before the first stage, between them, or after the second gives the same numbers: measured agreement to 8.9e-16 on the oracle input, i.e. floating-point noise. Worth knowing before someone "fixes" the placement.

No period options — the four numbers are the study

column and prefix are the whole option list. 35 / 20 / 10 with the ×10 are DecisionPoint's published PMO; a version with other lengths is a double-smoothed ROC, which is percentChange plus two movingAverage calls and should say so at the call site. (This is the kst decision applied to a second fixed-parameter study — with one asymmetry worth naming: kst does expose signalPeriod, because vendors differ on it there. DecisionPoint's 10 is not similarly contested, so it stays fixed here.)

Definition, verified

No TA-Lib function, so the oracle is a pandas replication with the analytic first-valid bars asserted and three measured separations — the span-EMA stages, the custom-smoothed signal, and the ×10 placement.

Warm-up

The rate of change costs bar 0; each custom stage then emits once it has consumed its own n finite samples, stepping over the previous stage's warm-up rather than seeding on it. So on gap-free input the line first lands on bar 54 (1 + 35 − 1 + 20 − 1) and the signal on bar 63. Length-preserving; each column emitted where it is defined.

Edges

• Scale-invariant, not shift-invariant. The rate of change is a ratio, so scaling every price leaves both columns unchanged; adding a constant changes the ratio and moves them. Both pinned as property tests.
• A zero previous price → undefined for that bar's rate of change, inherited from percentChangeValues. Unreachable on prices; reachable when column is a study output that crosses zero.
• A leading gap shifts the start; an interior gap costs the bar and the bar after it (the rate of change reads a predecessor), and the two recursions then skip and carry on — the ema family's rule, not Wilder's, so nothing propagates to the end.
• Not bounded. It is a percent rate of change times ten, smoothed, so its scale depends entirely on the instrument's daily moves.