wickra/docs/wiki/indicators/momentum-oscillators/Indicator-Pmo.md

PMO

Price Momentum Oscillator — Carl Swenlin's DecisionPoint PMO line: a doubly-smoothed rate of change.

Quick reference

Field	Value
Family	Momentum Oscillators
Input type	f64 (single close)
Output type	f64
Output range	unbounded around zero
Default parameters	(smoothing1 = 35, smoothing2 = 20) (Python)
Warmup period	2
Interpretation	Smoothed momentum; zero-line and signal-line crosses are the signals.

Formula

roc_t      = (price_t / price_{t−1} − 1) · 100
smoothed_t = customEMA(roc, smoothing1)_t
PMO_t      = customEMA(10 · smoothed, smoothing2)_t

customEMA is the DecisionPoint smoothing: an exponential average whose smoothing constant is 2 / period (not the textbook 2 / (period + 1)), seeded from its first input. The 1-bar percentage change is smoothed once, scaled by 10, then smoothed again.

The classic PMO signal line is a 10-period EMA of this PMO line. It is deliberately not bundled in — compose it yourself with Chain and an Ema(10).

Parameters

Name	Type	Default	Valid range	Description
smoothing1	usize	35 (Python)	>= 2	First smoothing period (applied to ROC). 0 errors with Error::PeriodZero; 1 with Error::InvalidPeriod.
smoothing2	usize	20 (Python)	>= 2	Second smoothing period (applied to 10 · smoothed). Same error rules.

smoothing = 1 is rejected because the smoothing constant 2 / 1 = 2 would exceed 1. The Python binding defaults the pair to (35, 20) via #[pyo3(signature = (smoothing1=35, smoothing2=20))]. The periods property returns (smoothing1, smoothing2).

Inputs / Outputs

From crates/wickra-core/src/indicators/pmo.rs:

impl Indicator for Pmo {
    type Input = f64;
    type Output = f64;
    // update(&mut self, input: f64) -> Option<f64>
}

A single f64 close in, an Option<f64> out. Python maps this to float | None / numpy.ndarray (NaN warmup); Node to number | null / Array<number> (NaN warmup).

Warmup

Pmo::new(s1, s2).warmup_period() == 2. The first ROC needs a previous price, and both customEMAs seed from their very first input, so the first non-None output lands on the second update(). Note this is the first defined value; the doubly-smoothed series only stabilises after many more bars, so treat early readings as unsettled.

Edge cases

• Constant series. A flat series gives roc = 0 on every bar, so both smoothings stay at 0 and PMO is 0.0 (constant_series_yields_zero pins this).
• Zero previous price. A ratio against a 0.0 prior price is undefined; roc is treated as 0 for that bar.
• NaN / infinity inputs. Non-finite inputs are silently dropped; the smoothing chains are not advanced.
• Reset. pmo.reset() clears the previous price and both EMAs.

Examples

Rust

use wickra::{Indicator, Pmo};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut pmo = Pmo::new(35, 20)?;
    println!("{:?}", pmo.update(100.0)); // no previous price yet
    println!("{:?}", pmo.update(101.0)); // first defined PMO
    Ok(())
}

Output:

None
Some(10.0)

The first update only records the price. The second produces roc = 1.0%; each customEMA seeds from its first input, so the inner EMA emits 1.0, the ×10 scaling gives 10.0, and the outer EMA seeds at 10.0 — hence PMO = 10.0 on the first defined bar. Early values are seed artefacts: the double smoothing only settles after many more bars. This matches the first_emission_at_second_update test in crates/wickra-core/src/indicators/pmo.rs.

Python

import numpy as np
import wickra as ta

pmo = ta.PMO()  # (smoothing1=35, smoothing2=20)
prices = 100.0 * 1.01 ** np.arange(120)  # steady uptrend
out = pmo.batch(prices)
print("last > 0:", out[-1] > 0)

Output:

last > 0: True

Node

const ta = require('wickra');
const pmo = new ta.PMO(35, 20);
const prices = Array.from({ length: 120 }, (_, i) => 100 * 1.01 ** i);
console.log('last:', pmo.batch(prices).at(-1));

Interpretation

Pmo is a smoothed momentum line. The DecisionPoint reads are: PMO crossing its zero line (momentum changing sign), PMO crossing its signal line (a 10-EMA of PMO — build it with Chain), and PMO turning up/down from an extreme. Because the rate of change is taken in percentage terms, PMO values are comparable across instruments — unlike raw Mom.

Common pitfalls

• Trusting the first few values. warmup_period() is 2, but that is only the first defined output — the double smoothing needs many bars to settle. Discard the early ramp.
• Expecting a bundled signal line. PMO here is the single PMO line; add Ema(10) via Chain for the signal.

References

Carl Swenlin, DecisionPoint Price Momentum Oscillator. The 2 / period "custom smoothing", the ×10 scaling and the conventional (35, 20) periods follow the published DecisionPoint definition.

See also

• Indicator-Roc.md — the raw rate of change PMO smooths.
• Indicator-Tsi.md — another double-smoothed momentum oscillator.
• Indicator-Chaining.md — how to add the signal-line EMA.
• Indicators-Overview.md — the full taxonomy.