- **Similar:** [KChannel](../kchannel/kchannel.md), [STBands](../stbands/stbands.md) | **Complementary:** ADX to distinguish trend vs range | **Trading note:** Volatility-normalized symmetric bands using ATR; adapts to true volatility including gaps.
ATR Bands create a volatility-adaptive envelope by projecting Wilder's Average True Range above and below a central Simple Moving Average. Unlike fixed-percentage envelopes or standard-deviation bands, ATR Bands use True Range to measure volatility, making them robust for assets with gaps, pre-market moves, and 24/7 trading where the "hidden" volatility between bars is significant. The True Range captures the maximum of intra-bar range, gap-up distance, and gap-down distance, ensuring that overnight gaps contribute fully to band width even when the current bar's open-to-close range is narrow.
J. Welles Wilder introduced Average True Range in *New Concepts in Technical Trading Systems* (1978), primarily as a trailing stop mechanism (the "Volatility Stop") and as a component of the Average Directional Index (ADX). Wilder used his own smoothing method, now known as RMA or Wilder's Smoothing, which is equivalent to an EMA with $\alpha = 1/n$. Futures traders in the 1980s quickly realized that projecting ATR above and below a trend-following moving average created a practical channel answering the question: "How far can price move from the average before it is statistically abnormal?"
ATR Bands differ from Keltner Channels only in the center line: ATR Bands use SMA, Keltner uses EMA. Some implementations use SMA-based ATR averaging instead of Wilder's smoothing. The QuanTAlib implementation uses Wilder's smoothing (RMA) for ATR with a warmup compensator for accurate early values, and SMA for the center line.
The SMA uses a circular buffer for $O(1)$ running sums. The ATR uses recursive IIR smoothing, also $O(1)$. True Range computation requires retaining the previous close. Total: $O(1)$ per bar with one buffer of size $n$ for the SMA.
