Awesome Oscillator Histogram

The bar-to-bar momentum of the AwesomeOscillator: AO_t − AO_{t−lookback}. This is the value behind the coloured histogram bars on Bill Williams' charts — positive means AO is rising (the histogram "greens up"), negative means it is falling.

Quick reference

Field	Value
Family	Price Oscillators
Input type	Candle (uses high and low for the median price)
Output type	f64
Output range	unbounded around zero
Default parameters	fast = 5, slow = 34, lookback = 1 (classic())
Warmup period	slow + lookback (35 for the defaults)
Interpretation	Positive: AO rising; negative: AO falling

Formula

median  = (high + low) / 2
AO      = SMA(median, fast) − SMA(median, slow)
AOHist  = AO_t − AO_{t−lookback}

The histogram reports the rate of change of the Awesome Oscillator over a lookback window. The classic one-bar delta (lookback = 1) is the coloured histogram every charting package draws under the AO.

This is distinct from the two related indicators Wickra ships: the raw AwesomeOscillator is AO itself, and the AcceleratorOscillator is AO − SMA(AO, 5). The histogram instead differences AO against its own past.

See crates/wickra-core/src/indicators/awesome_oscillator_histogram.rs (the update is at awesome_oscillator_histogram.rs:89).

Parameters

Name	Type	Default	Valid range	Source	Description
fast	usize	5	>= 1, < slow	awesome_oscillator_histogram.rs:55	Fast SMA length of the underlying AO.
slow	usize	34	>= 1, > fast	awesome_oscillator_histogram.rs:55	Slow SMA length of the underlying AO.
lookback	usize	1	>= 1	awesome_oscillator_histogram.rs:55	Momentum window: how many bars back AO is differenced against.

Any zero period returns Error::PeriodZero; fast >= slow returns Error::InvalidPeriod. AwesomeOscillatorHistogram::classic() is (5, 34, 1) (awesome_oscillator_histogram.rs:75). The Node/WASM constructor's third argument is named smaPeriod for backward compatibility, but it is this momentum lookback.

Inputs / Outputs

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

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

Only high and low are read (the AO uses the median price), so both native bindings take just those two series. Python streams as float | None and batches AwesomeOscillatorHistogram(fast, slow, lookback).batch(high, low) to a 1-D array.array('d') (NaN warmup). Node streams as number | null via update(high, low) and batches batch(high, low).

Warmup

warmup_period() returns slow + lookback. The AO first emits at slow candles; lookback more AO values are then needed before AO_t − AO_{t−lookback} can be formed. For the classic (5, 34, 1) that is 34 + 1 = 35. The unit tests accessors_and_metadata (classic().warmup_period() == 35) and warmup_emits_first_value_at_warmup_period ((2, 4, 2) → warmup 6: first five outputs None, out[5] is Some) pin this.

Edge cases

• Constant series. A flat median drives AO to 0, so its momentum is 0. Unit test constant_series_yields_zero.
• Equals the AO delta. The histogram equals AO_t − AO_{t−lookback} bar for bar. Unit test equals_ao_difference.
• Zero period. Any zero argument returns Err(Error::PeriodZero). Unit test rejects_zero_period.
• fast >= slow. Returns Err(Error::InvalidPeriod). Unit test rejects_fast_geq_slow.
• Reset. reset() clears both the AO and the lookback history. Unit test reset_clears_state.

Examples

Rust

use wickra::{AwesomeOscillatorHistogram, BatchExt, Candle, Indicator};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // A flat market: AO is zero, so its momentum (the histogram) is zero.
    let candles: Vec<Candle> = (0..10)
        .map(|i| Candle::new(42.0, 42.5, 41.5, 42.0, 1.0, i).unwrap())
        .collect();
    let mut hist = AwesomeOscillatorHistogram::new(3, 5, 1)?;
    let out = hist.batch(&candles);
    println!("warmup_period = {}", hist.warmup_period());
    println!("out[4] = {:?}, out[5] = {:?}", out[4], out[5]);
    Ok(())
}

Output:

warmup_period = 6
out[4] = None, out[5] = Some(0.0)

With (fast, slow, lookback) = (3, 5, 1) the warmup is 5 + 1 = 6: indices 0..5 are None, and from index 5 the flat series yields Some(0.0) — matching the warmup_emits_first_value_at_warmup_period and constant_series_yields_zero unit tests.

Python

import wickra as ta

high = [42.5] * 10
low = [41.5] * 10
hist = ta.AwesomeOscillatorHistogram(3, 5, 1)
out = hist.batch(high, low)
print('out[5]:', out[5])

Output:

out[5]: 0.0

Node

const wickra = require('wickra');

const high = Array.from({ length: 10 }, () => 42.5);
const low = Array.from({ length: 10 }, () => 41.5);
const hist = new wickra.AwesomeOscillatorHistogram(3, 5, 1);
console.log('out[5]:', hist.batch(high, low)[5]);

Output:

out[5]: 0

Streaming

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

let mut hist = AwesomeOscillatorHistogram::classic(); // (5, 34, 1)
let feed: Vec<Candle> = Vec::new(); // your live OHLCV candle feed
for bar in feed {
    if let Some(h) = hist.update(bar) {
        // h > 0: AO rose this bar (greening histogram); h < 0: AO fell
        let _ = h;
    }
}

Interpretation

1. Histogram colour. Each bar is AO_t − AO_{t−lookback}: positive bars are the "green" rising-momentum bars, negative bars the "red" falling ones.
2. Zero-line cross. A cross from negative to positive marks AO turning up; because it differences AO, the histogram turns before AO itself crosses zero — an earlier (and noisier) signal.
3. Tune the lookback. lookback = 1 is the classic one-bar delta; a larger lookback smooths the histogram into a slower rate-of-change read.

Common pitfalls

• Treating it as momentum. It is the change in momentum: a positive histogram with a still-negative AO means momentum is decelerating, not yet bullish.
• Confusing it with the Accelerator. AcceleratorOscillator is AO − SMA(AO, 5); this histogram is AO_t − AO_{t−lookback}. Different constructions, different signals.

References

• Bill Williams, New Trading Dimensions, Wiley (1998) — the Awesome Oscillator and its histogram of bar-to-bar change.

See also

• AwesomeOscillator — the momentum line itself.
• AcceleratorOscillator — AO − SMA(AO, 5).
• Alligator — Williams' trend filter.
• Indicators-Overview — the full taxonomy.