Bill Williams Indicators

ta4j 0.22.3 adds a complete Bill Williams indicator stack so you can model trend context, breakout structure, and participation in one workflow.

What this suite is (ta4j view)

In ta4j, the Bill Williams stack is implemented as composable indicators that plug directly into the standard Indicator + Rule + Strategy pipeline:

• trend context from AlligatorIndicator
• structure confirmation from FractalHighIndicator / FractalLowIndicator
• participation/expansion context from GatorOscillatorIndicator and MarketFacilitationIndexIndicator

This matters in ta4j because each component can be backtested, combined with non-Bill-Williams indicators, and ranked with the same criteria stack used elsewhere in the library.

Included indicators

• AlligatorIndicator – displaced SMMAs on median price (jaw, teeth, lips)
• FractalHighIndicator / FractalLowIndicator – confirmed fractal pivots (default 2/2 windows)
• GatorOscillatorIndicator – histogram spread between alligator lines
• MarketFacilitationIndexIndicator – Bill Williams MFI ((high - low) / volume)

Why and when this is useful

Use this suite when your ta4j strategy needs all three at once:

1. trend regime (sleeping vs trending),
2. explicit structure events (confirmed fractal breakouts),
3. participation filter (range expansion per volume).

Typical ta4j use cases:

• swing/trend-following systems that need structure-aware entries,
• breakout systems that want confirmation on fully formed bars,
• hybrid systems where Bill Williams signals gate another indicator family (for example MACD-V or VWAP rules).

Avoid relying on it alone in very low-volume instruments or ultra-short bar horizons where (high - low) / volume becomes unstable/noisy.

Canonical defaults

Alligator canonical settings in ta4j follow Bill Williams defaults:

• jaw: SMMA(13) shifted by 8
• teeth: SMMA(8) shifted by 5
• lips: SMMA(5) shifted by 3

Fractal defaults use 2 preceding + 2 following bars.

Look-ahead safety

Fractal indicators confirm on the current bar. When a fractal is confirmed at index i, the pivot is earlier. Use getConfirmedFractalIndex(i) to retrieve the pivot index explicitly.

This avoids accidental look-ahead bias when building entry/exit rules.

In ta4j terms: FractalHighIndicator and FractalLowIndicator are Indicator<Boolean> implementations, so they are event/confirmation signals, not direct price levels.

Example workflow

BarSeries series = ...;

AlligatorIndicator jaw = AlligatorIndicator.jaw(series);
AlligatorIndicator teeth = AlligatorIndicator.teeth(series);
AlligatorIndicator lips = AlligatorIndicator.lips(series);

FractalHighIndicator fractalHigh = new FractalHighIndicator(series);
FractalLowIndicator fractalLow = new FractalLowIndicator(series);

GatorOscillatorIndicator gatorUpper = GatorOscillatorIndicator.upper(series);
GatorOscillatorIndicator gatorLower = GatorOscillatorIndicator.lower(series);
MarketFacilitationIndexIndicator bwMfi = new MarketFacilitationIndexIndicator(series);

Strategy wiring pattern in ta4j

Num zero = series.numFactory().zero();

Rule trendUp = new OverIndicatorRule(lips, teeth)
        .and(new OverIndicatorRule(teeth, jaw));
Rule confirmedFractalBreakout = new BooleanIndicatorRule(fractalHigh);
Rule participation = new OverIndicatorRule(gatorUpper, zero)
        .and(new OverIndicatorRule(bwMfi, zero));

Rule entryRule = trendUp.and(confirmedFractalBreakout).and(participation);

Why this pattern works in ta4j:

• BooleanIndicatorRule consumes fractal confirmation events directly.
• OverIndicatorRule keeps numeric comparisons explicit and testable.
• Num values come from the series factory, keeping numeric type consistency.

For realistic backtests, set unstable bars high enough to cover all dependency warm-up periods (Alligator displacement + fractal windows + any added filters).

Typical interpretation:

1. Use alligator line ordering (lips > teeth > jaw or inverse) for trend context.
2. Use confirmed fractals for structure breakouts and invalidation levels.
3. Use gator and BW MFI to filter weak setups with low participation.

Practical notes

• MarketFacilitationIndexIndicator is not the same indicator as MoneyFlowIndexIndicator.
• AlligatorIndicator displacement is implemented without look-ahead (value at i reads smoothed value at i - shift).
• GatorOscillatorIndicator.upper(...) and .lower(...) provide the two histogram branches separately.
• For reproducible backtests, combine this toolkit with unstable-bar handling in Backtesting.
• For broader market-structure context (VWAP + support/resistance + Wyckoff), see VWAP, Support/Resistance, and Wyckoff Guide.