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Bill Williams Alligator

Classic trend moving-average classic williams

Trend-following indicator using three delayed smoothed moving averages.

Visual Example

Bill Williams Alligator — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Bill Williams Alligator indicator is a technical analysis tool that trend-following indicator using three delayed smoothed moving averages.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use to identify trend presence and direction. When the three Alligator lines are separated and fanning, the market is trending; when they converge or intertwine, the market is ranging.

Bill Williams introduced the Alligator in Trading Chaos (1995) as three offset SMAs with periods 13, 8, and 5 and offsets of 8, 5, and 3 bars. The three lines represent the Jaw, Teeth, and Lips of the Alligator. When the Alligator is sleeping (lines intertwined) no trade is taken; when it wakes and opens its mouth a trend trade is entered. — StockCharts ChartSchool

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

Implementation (quantwave-core/src/indicators/alligator.rs):

\[ \text{Jaw} = \text{SMMA}(13, 8), \text{Teeth} = \text{SMMA}(8, 5), \text{Lips} = \text{SMMA}(5, 3) \]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/alligator.json.

Parameters

Parameter Default Description
(none) — No tunable parameters for this detector.

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::ALLIGATOR;
use quantwave_core::traits::Next;

let mut ind = ALLIGATOR::new(14);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import ALLIGATOR

ind = ALLIGATOR(14)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_bill_williams_alligator(series: pl.Series) -> pl.Series:
    ind = qw.ALLIGATOR(14)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_bill_williams_alligator, return_dtype=pl.Float64).alias("bill_williams_alligator")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

  • Warm-up: first N bars may return NaN or partial state per implementation.
  • Parameter sensitivity: smaller periods increase noise; larger periods increase lag.
  • Sudden gaps or bad ticks can distort rolling windows — consider pre-filtering.
  • Single-series indicators ignore volume unless otherwise documented.
  • Validated via proptests against gold-standard vectors where available.
  • No look-ahead bias; streaming and Polars batch paths are bit-identical.

Boundary Behavior

Condition Behavior
Warm-up Leading bars return NaN until warmup_bars is satisfied.
period > len When period exceeds series length, output is all NaN.
NaN inputs NaN in input propagates to output (NaN out).
Invalid params Non-positive period or missing required params raise ValueError.
Empty data Empty input returns an empty result series.

Sources & References

Primary Source: https://chartschool.stockcharts.com/table-of-contents/technical-indicators-and-overlays/alligator

Implementation: quantwave-core/src/indicators/alligator.rs (ALLIGATOR / ALLIGATOR_METADATA). Parity: quantwave-core/tests/gold_standard/alligator.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.