wickra/docs/wiki/indicators/price-oscillators/Indicator-Ppo.md

PPO

Percentage Price Oscillator — MACD expressed as a percentage of the slow EMA, so readings are comparable across instruments.

Quick reference

Field	Value
Family	Price Oscillators
Input type	f64 (single close)
Output type	f64
Output range	unbounded around zero (percent)
Default parameters	(fast = 12, slow = 26) (Python)
Warmup period	slow
Interpretation	Percentage gap between a fast and slow EMA; zero-line crosses are signals.

Formula

PPO = 100 · (EMA_fast − EMA_slow) / EMA_slow

PPO is MacdIndicator divided by the slow EMA. That single change makes it scale-free: a PPO of 1.5 always means "the fast EMA is 1.5 % above the slow EMA", whether the instrument trades at $5 or $5000 — so PPO values can be compared across assets and across time, which raw MACD values cannot. The classic PPO signal line is a 9-period EMA of this PPO line; compose it with Chain and an Ema(9).

Parameters

Name	Type	Default	Valid range	Description
fast	usize	12 (Python)	>= 1, < slow	Fast EMA period.
slow	usize	26 (Python)	> fast	Slow EMA period.

fast must be strictly less than slow — otherwise new returns Error::InvalidPeriod. A zero period returns Error::PeriodZero. The Python binding defaults the pair to (12, 26); the periods property returns (fast, slow).

Inputs / Outputs

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

impl Indicator for Ppo {
    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

Ppo::new(fast, slow).warmup_period() == slow. Both EMAs are SMA-seeded; the slow EMA is the last to seed, at input slow, which is also when PPO emits its first value.

Edge cases

• Constant series. Both EMAs converge to the constant, so their gap — and PPO — is 0 (constant_series_yields_zero pins this).
• Zero slow EMA. A 0.0 slow EMA would divide by zero; PPO reports 0.0 for that bar instead.
• NaN / infinity inputs. Non-finite inputs are silently dropped; the EMAs are not advanced.
• Reset. ppo.reset() clears both EMAs and the cached value.

Examples

Rust

use wickra::{BatchExt, Indicator, Ppo};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut ppo = Ppo::new(12, 26)?;
    let prices: Vec<f64> = (1..=80).map(f64::from).collect();
    let out = ppo.batch(&prices);
    println!("warmup_period = {}", ppo.warmup_period());
    println!("last > 0: {}", out.last().unwrap().unwrap() > 0.0);
    Ok(())
}

Output:

warmup_period = 26
last > 0: true

In a rising series the fast EMA leads the slow EMA, so PPO is positive.

Python

import numpy as np
import wickra as ta

ppo = ta.PPO()  # (fast=12, slow=26)
prices = np.full(60, 100.0)  # flat series
print(ppo.batch(prices)[-1])  # both EMAs equal -> 0

Output:

0.0

Node

const ta = require('wickra');
const ppo = new ta.PPO(12, 26);
const prices = Array.from({ length: 80 }, (_, i) => 100 + i);
console.log('warmupPeriod:', ppo.warmupPeriod());

Interpretation

Ppo is read exactly like MACD: the zero-line cross (fast EMA crossing the slow EMA), the signal-line cross (PPO crossing its own 9-EMA), and histogram-style divergence. Its advantage over MACD is comparability — a PPO scan across a watchlist ranks instruments by relative trend strength, which a MACD scan cannot do because MACD is in each instrument's own price units.

Common pitfalls

• Expecting a bundled signal line. Ppo here is the single PPO line; add Ema(9) via Chain for the signal line and histogram.
• fast >= slow. The constructor rejects it — the fast EMA must be the faster one.

References

Gerald Appel's MACD, re-expressed as a percentage. The implementation follows the standard PPO definition and matches TA-Lib's PPO.

See also

• Indicator-MacdIndicator.md — the price-unit original, with a bundled signal line and histogram.
• Indicator-Ema.md — the underlying average.
• Indicators-Overview.md — the full taxonomy.