Williams Alligator (ALLIGATOR)

Summary

Bill Williams' Alligator (Trading Chaos, 1995): three smoothed moving averages of the median price. The Jaw, Teeth and Lips are each drawn a few bars ahead of the bar that computed it. When the three lines are intertwined the alligator sleeps and the market has no trend; when they fan out in order, Lips above Teeth above Jaw or the reverse, it is feeding and a trend is under way. Price crossing back into the lines is read as the trend tiring.

The Alligator is a leg of Williams' Profitunity system, alongside the Awesome Oscillator (AO) and the Accelerator/Decelerator (AC).

Chart

Chart metadata i

Drawn on the price pane over candles, with outJaw as a solid line moved 8 bars forward, outTeeth as a solid line moved 5 bars forward and outLips as a solid line moved 3 bars forward.

Metadata flags used: overlap · inPriceHL: high, low · outJaw: line, display_shift (+8) · outTeeth: line, display_shift (+5) · outLips: line, display_shift (+3)

Reference data (CSV) · Chart (SVG)

Formula

median_t = ( high_t + low_t ) / 2
Jaw_t = SMMA(median, jawPeriod)_t
Teeth_t = SMMA(median, teethPeriod)_t
Lips_t = SMMA(median, lipsPeriod)_t

SMMA is Wilder's smoothed moving average (RMA): seeded with the simple average of its first n values, then SMMA_t = SMMA_t−1 + ( x_t − SMMA_t−1 ) / n.

Notes

Each line is TA_RMA of TA_MEDPRICE over its own period. Williams draws the lines ahead of price; that is a display shift: TA_ALLIGATOR_DisplayShift reports each line's shift, and it changes nothing about the values, the lookback or the returned range. Every output is written at the bar that computed it, so the last shift values of a line are the part a chart draws past the last bar.
All three lines start at the bar of the longest period, and each shorter line seeds over the bars its own lookback reaches back from there, not at the first bar of the series. A chart that seeds every line at the first bar draws different short lines until the seed has decayed; setting the RMA unstable period closes the gap.

Inputs

inHigh — High price of each bar
inLow — Low price of each bar

Outputs

outJaw — Jaw: the slowest line, drawn ahead by the jaw shift
outTeeth — Teeth: the middle line, drawn ahead by the teeth shift
outLips — Lips: the fastest line, drawn ahead by the lips shift

Parameters

Parameter	Type	Default	Accepted values	Description
`optInJawPeriod`	integer	13	1–100000	Number of bars in the jaw's smoothed moving average.
`optInJawShift`	integer	8	0–100000	Bars ahead of the computing bar at which a chart draws the jaw.
`optInTeethPeriod`	integer	8	1–100000	Number of bars in the teeth's smoothed moving average.
`optInTeethShift`	integer	5	0–100000	Bars ahead of the computing bar at which a chart draws the teeth.
`optInLipsPeriod`	integer	5	1–100000	Number of bars in the lips' smoothed moving average.
`optInLipsShift`	integer	3	0–100000	Bars ahead of the computing bar at which a chart draws the lips.

Properties

Numerical Stability: Initial Unstable Period — Inherited from RMA, which ALLIGATOR computes internally; tunable via RMA's unstable period.


✅ Overlap Input i
☐ Independent Y-Axis
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1
✅ Display Shift i
☐ Uses Transcendental
☐ Input Must Be Positive

Example

#include <stdio.h>
#include <ta_libc.h>

int n = 252;
double high[252]; /* your data, oldest first */
double low[252]; /* your data, oldest first */
double jaw[252], teeth[252], lips[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_ALLIGATOR( 0, n - 1, high, low, 13, 8, 8, 5, 5, 3, &outBegIdx, &outNBElement, jaw, teeth, lips );
printf( "%d values from bar %d; last jaw = %f\n", outNBElement, outBegIdx, jaw[outNBElement - 1] );

Rust

use ta_lib::Core;

let high = vec![0.0; 252]; // your data, oldest first
let low = vec![0.0; 252]; // your data, oldest first
let mut jaw = vec![0.0; 252];
let mut teeth = vec![0.0; 252];
let mut lips = vec![0.0; 252];

let core = Core::new();
let range = core.alligator(0, high.len() - 1, &high, &low, 13, 8, 8, 5, 5, 3,
                           &mut jaw, &mut teeth, &mut lips)?;
println!("{} values from bar {}; last jaw = {}", range.count, range.beg_idx, jaw[range.count - 1]);

Java

import io.github.talib.Core;
import io.github.talib.OutRange;

double[] high = new double[252]; // your data, oldest first
double[] low = new double[252]; // your data, oldest first
double[] jaw = new double[252];
double[] teeth = new double[252];
double[] lips = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.alligator(0, high.length - 1, high, low, 13, 8, 8, 5, 5, 3, jaw, teeth, lips);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last jaw = " + jaw[r.count() - 1]);

using System;
using TALib;

var high = new double[252]; // your data, oldest first
var low = new double[252]; // your data, oldest first
var jaw = new double[252];
var teeth = new double[252];
var lips = new double[252];

var core = Core.Default;
OutRange r = core.Alligator(0, high.Length - 1, high, low, 13, 8, 8, 5, 5, 3, jaw, teeth, lips);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last jaw = {jaw[r.Count - 1]}");

TypeScript

import { alligator } from 'ta-lib';

const high = new Float64Array(252); // your data, oldest first
const low = new Float64Array(252); // your data, oldest first

const { begIdx, outJaw, outTeeth, outLips } = alligator({ high, low }, {
  jawPeriod: 13,
  jawShift: 8,
  teethPeriod: 8,
  teethShift: 5,
  lipsPeriod: 5,
  lipsShift: 3,
});
console.log(outJaw.length + ' values from bar ' + begIdx + '; last outJaw = ' + outJaw[outJaw.length - 1]);

Implementation

Added in 0.8.4.

TA-Lib Definition: alligator.c · alligator.yaml

Native	File
C	`ta_ALLIGATOR.c`
Rust	`alligator.rs`
Java	`Core_ALLIGATOR.java`
C#	`Core_ALLIGATOR.cs`
TypeScript	`alligator.ts`

Python: talib.ALLIGATOR, see ta-lib-python.

TA-Lib is also available for R and more using a wrapper.

Aliases

williams alligator, bill williams alligator, jaw teeth lips

References

Bill Williams, Trading Chaos, 1995
Bill Williams, New Trading Dimensions, 1998
MetaTrader 5 — Alligator