- Donchian Channels track the highest high and lowest low over a fixed lookback period, defining the absolute price boundaries within which an asset has traded.
- **Similar:** [PC](../pc/pc.md), [UChannel](../uchannel/uchannel.md) | **Complementary:** Volume on breakouts; ATR for position sizing | **Trading note:** Pure price-based highest high/lowest low; used in the original Turtle Trading system.
Donchian Channels track the highest high and lowest low over a fixed lookback period, defining the absolute price boundaries within which an asset has traded. Unlike volatility-based bands that compute statistical dispersion, Donchian Channels represent actual historical extremes — the literal "price box." The implementation uses monotonic deques for $O(1)$ amortized sliding-window max/min, ensuring that computing a 500-period channel costs no more than a 20-period one. The midpoint of the upper and lower bands serves as a simple trend bias indicator.
Richard Donchian developed this channel in the 1960s while managing one of the first publicly held commodity funds. Known as the "father of trend following," Donchian pioneered systematic trading in an era dominated by discretionary methods. His "4-week rule" (buy on a 20-day high, sell on a 20-day low) became one of the earliest documented mechanical trading systems.
The indicator achieved legendary status through the Turtle Trading experiment in 1983. Richard Dennis and William Eckhardt recruited novice traders and taught them a mechanical system built on channel breakouts. The Turtles reportedly earned over $100 million. Curtis Faith's *Way of the Turtle* (2007) revealed the core system: enter on 20-day breakouts, exit on 10-day counter-breakouts. The simplicity is the feature: no predictions, no fitting, no optimization — just price breaking through defined boundaries.
The naive approach scans the entire window for each bar: $O(n)$ per update. The monotonic deque (also called a sliding window max/min queue) maintains candidates in sorted order:
The bands stay flat until either a new extreme occurs or the old extreme exits the window. A band that hasn't moved in 15 bars is waiting for new information. This piecewise-constant behavior is the defining characteristic: unlike smoothed envelopes, Donchian Channels are discontinuous, stepping only at regime transitions.
Each element enters and exits each deque exactly once over the full series, so worst-case per-bar is $O(n)$ but amortized cost is $O(1)$. Memory: two deques of up to $n$ index entries + two circular buffers of $n$ values.
### Batch Mode (SIMD Analysis)
Monotonic deques are inherently sequential (deque state depends on insertion order). No SIMD parallelization across bars is possible:
