QuanTAlib/lib/channels/accbands/accbands.md

ACCBANDS: Acceleration Bands

"Price creates its own envelope, expanding with potential and contracting with consensus."

Acceleration Bands (ACCBANDS) serve as an adaptive volatility envelope based on the high-low range rather than standard deviation. Unlike Bollinger Bands which use close-to-close variance, Acceleration Bands utilize the intra-bar high-low spread to gauge volatility, creating channels that accommodate the full price excursion of the underlying asset.

Historical Context

Developed by Price Headley and detailed in Big Trends in Trading (2002), Acceleration Bands addressed the need for a breakout-specific envelope. Headley observed that standard deviation often lagged in fast-moving breakout scenarios. By incorporating the High and Low prices directly into the band width calculation — using a per-bar normalized range width — he created a system that reacts immediately to range expansion, often serving as a trigger for trend-following entries when price closes outside the bands.

Architecture & Physics

The indicator applies a per-bar width adjustment based on the normalized range w = (H-L)/(H+L) before averaging. This means wider-range bars contribute proportionally more to band expansion. Three Simple Moving Averages (adjusted high, adjusted low, close) construct the bands.

Calculation Steps (Headley's Formula)

1. Per-bar normalized width:

   w_t = \frac{High_t - Low_t}{High_t + Low_t}

2. Adjusted prices per bar:

   AdjHigh_t = High_t \times (1 + Factor \times w_t) AdjLow_t = Low_t \times (1 - Factor \times w_t)

3. Band Construction:

   Upper_t = SMA(AdjHigh, n) Lower_t = SMA(AdjLow, n) Middle_t = SMA(Close, n)

   Where n = period (default 20), Factor = multiplier (default 4.0).

Performance Profile

The implementation uses three independent circular buffers (adjusted high, adjusted low, close) to maintain O(1) complexity for the moving averages.

Operation Count - Single value

Operation	Count	Cost (cycles)	Subtotal
ADD/SUB	10	1	10
MUL	4	3	12
DIV	4	15	60
Total	18	—	~82 cycles

Operation Count - Batch processing

SIMD optimization is applied to the sum resynchronization, though the recursive nature of the SMAs limits full vectorization of the state maintenance.

Operation	Scalar Ops	SIMD Ops (AVX/SSE)	Acceleration
Band Construction	3N	3N/VectorSize	~4-8×
SMAs	3N	3N	1×

Validation

Library	Status	Notes
TA-Lib	✅	All three bands match exactly (same Headley formula)
Internal	✅	Streaming/Batch/Span match exactly

Usage & Pitfalls

• Trend Definition: Headley defines a breakout as two consecutive closes outside the bands.
• Parameter Sensitivity: The default factor of 4.0 matches TA-Lib and Headley's original. Lower factors (e.g., 2.0) produce tighter bands; higher factors (e.g., 6.0) may be needed for crypto/FX.
• Lag: Inherits the lag of the underlying SMA. Not suitable for ultra-high-frequency reacting.
• Range vs Variance: Because it uses High-Low range, it is more sensitive to "wicks" or momentary spikes than close-based envelopes.
• Division by Zero: When High + Low = 0 (price is zero), the normalized width defaults to 0.

API

classDiagram
    class AccBands {
        +TValue Last
        +TValue Upper
        +TValue Lower
        +bool IsHot
        +event Pub
        +Update(TBar bar) TValue
        +Update(TBarSeries source) tuple
        +Batch(TBarSeries source, int p, double f) tuple
    }

Class: AccBands

Parameter	Type	Default	Range	Description
period	int	—	>0	Lookback period for SMAs.
factor	double	4.0	>0	Multiplier for normalized width.
source	TBarSeries	—	any	Initial input TBar data (optional).

Properties

• Last (TValue): The current middle band value (SMA of Close).
• Upper (TValue): The current upper band value (SMA of adjusted High).
• Lower (TValue): The current lower band value (SMA of adjusted Low).
• IsHot (bool): Returns true if valid data is available (warmup complete).

Methods

• Update(TBar input): Updates the indicator with a new bar.
• Update(TBarSeries source): Processes a full series.
• Batch(...): Static method for high-performance batch processing.

C# Example

using QuanTAlib;

// Initialize
var indicator = new AccBands(period: 20, factor: 4.0);

// Update Loop
foreach (var bar in bars)
{
    var result = indicator.Update(bar);
    
    // Use valid results
    if (indicator.IsHot)
    {
        Console.WriteLine($"{bar.Time}: Mid={result.Value:F2} Up={indicator.Upper.Value:F2} Low={indicator.Lower.Value:F2}");
    }
}