PGO

Pretty Good Oscillator — Mark Johnson's displacement of the close from its period-bar SMA, normalised by the period-bar EMA of the True Range. Roughly "how many ATR-equivalents is the close from its mean?".

Quick reference

Field	Value
Family	Price Oscillators
Input type	Candle (uses high, low, close)
Output type	f64
Output range	unbounded; in ATR-equivalent units around zero
Default parameters	period = 14
Warmup period	period (exact)
Interpretation	A +3 cross is Johnson's long entry, a −3 cross his short entry.

Formula

PGO_t = (close_t − SMA(close, period)_t) / EMA(TR_t, period)

The numerator is positive when the close is above its mean of the last period bars, negative when below. The denominator is the EMA-smoothed TrueRange, a volatility scale — so PGO normalises the displacement into ATR-equivalent units, making thresholds like ±3 comparable across instruments.

Parameters

Name	Type	Default	Constraint	Source
period	usize	14	>= 1	Pgo::new (pgo.rs:52)

period == 0 returns [Error::PeriodZero]. Python default comes from #[pyo3(signature = (period=14))]; the Node constructor takes period explicitly. The public class is PGO in both bindings.

Inputs / Outputs

use wickra::{Indicator, Pgo, Candle};
// Pgo: Input = Candle, Output = f64
const _: fn(&mut Pgo, Candle) -> Option<f64> = <Pgo as Indicator>::update;

• Python. update(candle) returns float | None; batch(high, low, close) returns a 1-D float64 np.ndarray with NaN warmup.
• Node. update(high, low, close) returns number | null; batch(high, low, close) returns an Array<number> with NaN warmup.

Warmup

warmup_period() returns period. The SMA of close and the EMA of the True Range both reach readiness at exactly period candles, so PGO emits its first value on candle period (index period − 1). Pinned by warmup_emits_first_value_at_period (period 3: candles 1–2 return None, candle 3 emits).

Edge cases

• Flat close. A constant close makes close == SMA, so the numerator is 0 and PGO = 0 regardless of the (non-zero) TR denominator (test flat_close_yields_zero_numerator).
• Rising series. The latest close sits above its SMA, so PGO > 0 (test close_above_mean_is_positive).
• Zero True Range. A window of single-point candles (high == low == close) drives EMA(TR) to 0; PGO then holds its previous value (and stays None if no value has been emitted yet — test zero_tr_holds_value).
• Reset. reset() clears the SMA, the True Range, the EMA and the held value.

Examples

Rust

use wickra::{Candle, Indicator, Pgo};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut pgo = Pgo::new(5)?;
    let mut last = None;
    for i in 0..20 {
        let c = 10.0 + i as f64;                // rising close
        last = pgo.update(Candle::new(c, c + 0.5, c - 0.5, c, 1.0, i)?);
    }
    println!("{last:?}"); // Some(positive) — close above its SMA
    Ok(())
}

Python

import numpy as np
import wickra as ta

pgo = ta.PGO(14)
out = pgo.batch(high, low, close)  # 1-D series, NaN for the first 13 rows

Node

const ta = require('wickra');
const pgo = new ta.PGO(14);
const v = pgo.update(101.0, 99.0, 100.5); // null during warmup, else a number

Interpretation

PGO answers "how stretched is price from its own mean, in volatility units?":

1. Mean-reversion / breakout thresholds. Johnson's heuristic uses ±3: a cross above +3 is a momentum long, a cross below −3 a momentum short — treating large normalised displacement as a breakout, not an exhaustion.
2. Cross-instrument comparability. Because the displacement is divided by an ATR-like scale, the ±3 threshold means roughly the same thing on a quiet bond future as on a volatile altcoin.

Common pitfalls

• Reading raw price distance. PGO is normalised by volatility — a reading of 2 means "2 ATR-equivalents above the mean", not 2 price units.
• Mistaking it for an oscillator with fixed bounds. Despite the name, PGO is unbounded; only the ±3 convention gives it working thresholds.

References

• Mark Johnson, "Pretty Good Oscillator", Technical Analysis of Stocks & Commodities, 1995.

See also

• Atr / TrueRange — the volatility scale in the denominator.
• Cci — another mean-displacement-over-dispersion oscillator (uses mean absolute deviation instead of ATR).
• ZScore — displacement normalised by standard deviation rather than ATR.