QQE

QQE — Quantitative Qualitative Estimation: a smoothed RSI with an "ATR of the RSI" trailing line, for cleaner momentum crossover signals.

Quick reference

Field	Value
Family	Momentum Oscillators
Input type	f64 (single price)
Output type	QqeOutput { rsi_ma, trailing_line }
Output range	[0, 100]-ish (RSI-scale); both lines move together
Default parameters	rsi_period (14), smoothing (5), factor (4.236)
Warmup period (warmup_period())	rsi_period + smoothing + 2·(2·rsi_period−1) − 2 (72 for defaults)
Interpretation	Smoothed RSI vs. its volatility trailing stop.

Formula

rsi_ma   = EMA(RSI(price, rsi_period), smoothing)
atr_rsi  = |rsi_ma − rsi_ma_prev|
ma_atr   = EMA(atr_rsi, 2·rsi_period − 1)          // Wilder length
dar      = EMA(ma_atr, 2·rsi_period − 1) · factor  // smoothed band width

long_band  = (rsi_ma_prev > long_band_prev  && rsi_ma > long_band_prev)
             ? max(long_band_prev,  rsi_ma − dar) : rsi_ma − dar
short_band = (rsi_ma_prev < short_band_prev && rsi_ma < short_band_prev)
             ? min(short_band_prev, rsi_ma + dar) : rsi_ma + dar
trend      = cross-up of short_band → +1, cross-down of long_band → −1, else hold
trailing_line = trend == +1 ? long_band : short_band

QQE smooths the RSI, measures that smoothed line's own "ATR" (the smoothed absolute bar-to-bar change), and builds a trailing stop ±dar around it. The trailing line ratchets in the trend direction — only ever tightening until the smoothed RSI crosses it — exactly like a SuperTrend on the RSI. The rsi_ma crossing the trailing_line is the QQE signal.

Source: crates/wickra-core/src/indicators/qqe.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
rsi_period	usize	14	>= 1	qqe.rs:88	RSI period (also sets the Wilder length 2·rsi_period−1).
smoothing	usize	5	>= 1	qqe.rs:88	EMA smoothing of the RSI.
factor	f64	4.236	> 0, finite	qqe.rs:92	Trailing band width multiplier.

rsi_period/smoothing of 0 error with Error::PeriodZero; a non-positive or non-finite factor errors with Error::InvalidPeriod. (Python wickra.QQE(rsi_period, smoothing, factor); Node new ta.QQE(...).)

Inputs / Outputs

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

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

Two outputs per bar. Node: update(value) returns { rsiMa, trailingLine } | null; batch(values) returns a flat Array<number> of length n*2 ([rsiMa, trailingLine, …], NaN for warmup). Python: update(value) returns (rsi_ma, trailing_line) | None; batch(values) returns an (n, 2) ndarray.

Warmup

warmup_period() chains the component warmups: RSI (rsi_period + 1) → rsi_ma EMA → one bar to form the first atr_rsi → ma_atr EMA → dar EMA, giving rsi_period + smoothing + 2·(2·rsi_period − 1) − 2 = 72 for the defaults. Pinned by first_emission_matches_warmup (first Some exactly at warmup_period() − 1).

Edge cases

• Steady trend → both lines equal. A pure trend pins the RSI, so atr_rsi, ma_atr, and dar collapse to 0 and both lines equal the smoothed RSI; shown below and checked by trailing_line_below_rsi_ma_in_uptrend.
• Equivalence to the full recurrence. matches_naive_over_full_cycle replays the entire band/trend state machine over an up-range-down series and asserts both outputs match bar-for-bar.
• Bad params. rejects_bad_params pins each error path.
• Reset. reset_clears_state. Streaming/batch: batch_equals_streaming.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut qqe = Qqe::new(14, 5, 4.236)?;
    let prices: Vec<f64> = (1..=120).map(f64::from).collect();
    let last = qqe.batch(&prices).into_iter().flatten().last().unwrap();
    println!("warmup_period = {}", qqe.warmup_period());
    println!("rsi_ma={} trailing_line={}", last.rsi_ma, last.trailing_line);
    Ok(())
}

Output:

warmup_period = 72
rsi_ma=100 trailing_line=100

On a steady uptrend the RSI is pinned at 100; its "ATR" is 0, so dar = 0 and the trailing line sits exactly on the smoothed RSI at 100.

Python

import numpy as np
import wickra as ta

qqe = ta.QQE(14, 5, 4.236)
out = qqe.batch(np.arange(1.0, 121.0))   # (120, 2): [rsi_ma, trailing_line]
print("warmup_period =", qqe.warmup_period())
print(out[-1])

Output:

warmup_period = 72
[100. 100.]

Node

const ta = require('wickra');
const qqe = new ta.QQE(14, 5, 4.236);
const prices = Array.from({ length: 120 }, (_, i) => i + 1);
const out = qqe.batch(prices); // flat [rsiMa, trailingLine, …], NaN warmup
console.log('warmupPeriod:', qqe.warmupPeriod());
console.log(out.slice(-2)); // [100, 100]

Output:

warmupPeriod: 72
[ 100, 100 ]

Streaming

use wickra::{Indicator, Qqe};

let mut qqe = Qqe::new(14, 5, 4.236)?;
let mut last = None;
for i in 0..200 {
    last = qqe.update(100.0 + (f64::from(i) * 0.1).sin() * 8.0);
}
if let Some(v) = last {
    println!("rsi_ma={:.2} trailing_line={:.2}", v.rsi_ma, v.trailing_line);
}
# Ok::<(), Box<dyn std::error::Error>>(())

Interpretation

QQE is a momentum-crossover system, not a level oscillator. The signal is the smoothed RSI crossing its trailing line: rsi_ma crossing above trailing_line is a long trigger, crossing below a short trigger. Because the trailing line is a volatility-scaled stop on the RSI, it filters the small RSI wiggles that would trip a raw RSI level cross.

Typical uses:

1. Cross signals. rsi_ma vs trailing_line crossovers time entries; the dar band makes them robust to RSI noise.
2. Trend persistence. The ratcheting trailing line keeps you in a move until a genuine momentum reversal crosses it.
3. 50-line context. Combine crosses with the rsi_ma's position relative to 50 for a trend-filtered version.

Common pitfalls

• Treating trailing_line as overbought/oversold. It is a trailing stop on the RSI, not a fixed level; read crossovers, not absolute values.
• Long warmup. With the defaults QQE needs 72 bars to start (two stacked Wilder-length EMAs); ensure enough history.

References

Igor Livshin, "Quantitative Qualitative Estimation", 2010 — the QQE built on Wilder's RSI (1978).

See also

• Indicator-Rsi — the oscillator QQE smooths and trails.
• Indicator-SuperTrend — the same trailing-stop idea on price.
• Indicator-Rsx — another smoothed-RSI refinement.
• Indicators-Overview — the full taxonomy.