- Acceleration Bands construct a volatility envelope using the intra-bar high-low range rather than close-to-close standard deviation, creating chann...
- **Similar:** [BBands](../bbands/bbands.md), [KChannel](../kchannel/kchannel.md) | **Complementary:** ADX for trend strength | **Trading note:** Wider than Bollinger Bands; effective for breakout trading using high-low range volatility.
Acceleration Bands construct a volatility envelope using the intra-bar high-low range rather than close-to-close standard deviation, creating channels that accommodate the full price excursion of the underlying asset. Each bar's contribution to band width is normalized by price level ($w = (H-L)/(H+L)$), making the bands scale-invariant across instruments. Three independent Simple Moving Averages of the adjusted high, adjusted low, and close prices form the upper, lower, and middle bands respectively. Headley's original breakout rule declares a trend when price closes outside the bands for two consecutive bars.
Price Headley developed Acceleration Bands and detailed them in *Big Trends in Trading* (Wiley, 2002). Headley observed that standard deviation bands often lag in fast-moving breakout scenarios because they require several bars of expanded volatility before the bands visibly widen. By incorporating High and Low prices directly into the band width calculation through a per-bar normalized range, he created a system that reacts immediately to range expansion.
The normalization $w = (H-L)/(H+L)$ is the key design choice. Dividing range by the sum of high and low produces a dimensionless ratio that is comparable across any price level. A $5 stock with a $0.50 range and a $500 stock with a $50 range both produce $w = 0.05$. The default factor of 4.0 was Headley's empirically determined value for equity markets on daily timeframes, matching the TA-Lib reference implementation.
Three independent circular buffers maintain running sums for $O(1)$ streaming updates. Each bar requires computing $w_t$, the two adjusted prices, and three buffer updates.
ACCBANDS computes per-bar normalized width, two adjusted prices, and three independent SMA running sums:
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| ADD (H + L for denom) | 1 | 1 | 1 |
| SUB (H - L for range) | 1 | 1 | 1 |
| DIV (range / denom for w) | 1 | 15 | 15 |
| MUL (factor × w) | 1 | 3 | 3 |
| MUL (H × (1 + F·w), L × (1 - F·w)) | 2 | 3 | 6 |
| SUB (oldest from 3 running sums) | 3 | 1 | 3 |
| ADD (new value to 3 running sums) | 3 | 1 | 3 |
| DIV (sum / count, three SMAs) | 3 | 15 | 45 |
| **Total (hot)** | **15** | — | **~77 cycles** |
The three DIV operations dominate. When the denominator is zero ($H + L = 0$), a branch sets $w = 0$, adding one CMP.
### Batch Mode (SIMD Analysis)
The three SMA running sums are sequential. The per-bar width computation ($w$, adjusted prices) is independent across bars and vectorizable in a batch pre-pass:
