QuanTAlib/lib/channels/dc/dc.md

DC: Donchian Channels

The highest high and lowest low over a window — Donchian's simplicity captures breakout potential in two lines.

Property	Value
Category	Channel
Inputs	OHLCV bar (TBar)
Parameters	period
Outputs	Multiple series (Upper, Lower)
Output range	Tracks input
Warmup	period bars
PineScript	dc.pine

• 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, UChannel | Complementary: Volume on breakouts; ATR for position sizing | Trading note: Pure price-based highest high/lowest low; used in the original Turtle Trading system.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

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.

Historical Context

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.

Architecture & Physics

1. Upper Band (Sliding Window Maximum)

\text{Upper}_t = \max_{i=0}^{n-1}(H_{t-i})

2. Lower Band (Sliding Window Minimum)

\text{Lower}_t = \min_{i=0}^{n-1}(L_{t-i})

3. Middle Band

\text{Middle}_t = \frac{\text{Upper}_t + \text{Lower}_t}{2}

4. Monotonic Deque Algorithm

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:

For the max deque (upper band):

1. Remove indices outside the window from the front
2. Remove values \leq current High from the back (they can never be the maximum again)
3. Push current index to the back
4. The front element is always the maximum

Each element enters exactly once and exits at most once, yielding O(1) amortized per bar over any sequence of N updates.

5. Stale Extremes

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.

Mathematical Foundation

Parameters

Parameter	Description	Default	Constraint
period	Lookback window for high/low extremes (n)	20	> 0

Output Interpretation

Output	Description
upper	Highest high over the lookback (resistance)
lower	Lowest low over the lookback (support)
middle	Midpoint of channel (trend bias)

Performance Profile

Operation Count (Streaming Mode)

DC uses two monotonic deques for O(1) amortized sliding-window max/min:

Operation	Count	Cost (cycles)	Subtotal
CMP (expire stale front, max deque)	1	1	1
CMP (remove dominated back, max deque)	~1 avg	1	1
CMP (expire stale front, min deque)	1	1	1
CMP (remove dominated back, min deque)	~1 avg	1	1
ADD (upper + lower)	1	1	1
MUL (× 0.5 for middle)	1	3	3
Total (amortized)	~6	—	~8 cycles

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:

Optimization	Benefit
Deque operations	Sequential; amortized O(1) already optimal
Midpoint computation	Vectorizable in a post-pass with Vector<double>
Memory layout	Circular buffers are cache-friendly for sequential access

Resources

• Donchian, R. "High Finance in Copper." Financial Analysts Journal, 16(6), 1960. (Original channel concept)
• Faith, C. Way of the Turtle: The Secret Methods that Turned Ordinary People into Legendary Traders. McGraw-Hill, 2007. (Turtle Trading system)
• Covel, M. The Complete TurtleTrader. HarperBusiness, 2007.
• Cormen, T.H. et al. Introduction to Algorithms. MIT Press, 2009. (Monotonic deque / sliding window algorithms)