QuanTAlib/lib/channels/pchannel/pchannel.md

PCHANNEL: Price Channel

"The Turtles didn't need complex math. They needed to know when price broke out of its cage."

Price Channel (PC) tracks the highest high and lowest low over a lookback period, creating a price envelope that defines where the market has been. Functionally identical to Donchian Channels—same algorithm, different name. Unlike volatility-based bands (Bollinger, Keltner), Price Channel uses actual price extremes—no standard deviations, no averages of true range. The result: bands that represent real support and resistance levels traders actually watch. This implementation uses monotonic deques for O(1) amortized updates rather than the naive O(n) rescan that plagues most implementations.

Historical Context

Price Channel is the generic name for what Richard Donchian formalized in the 1960s while managing one of the first publicly held commodity funds. The indicator is also known as Donchian Channels, N-period high/low channels, or simply "breakout bands."

The "4-week rule" (buy on 20-day high, sell on 20-day low) became the foundation for systematic trend-following. The indicator gained fame 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 made over $100 million. Curtis Faith's book and subsequent leaks revealed the core: enter on 20-day breakouts, exit on 10-day counter-breakouts.

Most implementations compute max/min by scanning the entire lookback window on every bar—O(n) per update, O(n²) for a series. This works for period=20 but becomes painful for longer windows or real-time feeds. QuanTAlib uses monotonic deques that maintain running max/min in O(1) amortized time, enabling period=500+ without performance degradation.

Architecture & Physics

Price Channel consists of three components: upper band (highest high), lower band (lowest low), and middle band (their average).

1. Upper Band (Highest High)

Tracks the maximum high price over the lookback window:

U_t = \max_{i=0}^{n-1}(H_{t-i})

where H is the high price and n is the period. The upper band moves up immediately when a new high occurs, but only drops when the previous highest high exits the lookback window.

2. Lower Band (Lowest Low)

Tracks the minimum low price over the lookback window:

L_t = \min_{i=0}^{n-1}(L_{t-i})

where L is the low price. The lower band drops immediately on new lows but only rises when the previous lowest low exits the window.

3. Middle Band

The arithmetic mean of the upper and lower bands:

M_t = \frac{U_t + L_t}{2}

This represents the "equilibrium" price over the lookback period.

Monotonic Deque Algorithm

Instead of rescanning the window on each bar, the implementation maintains two monotonic deques:

1. Deque (Max): Valid indices of decreasing values. Front is always the Max.
2. Deque (Min): Valid indices of increasing values. Front is always the Min.
3. Update:
   • Remove old indices from front (expired).
   • Remove values from back that are superseded by new value.
   • Add new value to back.

Complexity: Each element is added once and removed at most once. Total work for N bars is O(N), averaging O(1) per bar.

Performance Profile

Operation Count (Streaming Mode, Scalar)

Per-bar cost using monotonic deque optimization:

Operation	Count	Cost (cycles)	Subtotal
CMP (Bound checks)	4	1	4
ADD (Index update)	1	1	1
MUL (Average)	1	3	3
Deque Maint.	~2	1	~2
Total	8	—	~10 cycles

Complexity: O(1) amortized.

Batch Mode (512 values, SIMD/FMA)

Finding max/min over sliding windows has limited SIMD benefit due to sequential dependency and the efficiency of the scalar deque algorithm.

Operation	Scalar Ops	SIMD Benefit	Notes
Max/Min update	4	1×	Deque-based, sequential
Middle band	2	2×	ADD + MUL parallelizable

Mode	Cycles/bar	Total (512 bars)	Improvement
Scalar streaming	10	5,120	—
Partial SIMD	~8	~4,096	~20%

Validation

Library	Status	Notes
TA-Lib	-	No implementation
Skender	-	No implementation (uses Donchian)
Tulip	-	No implementation
Ooples	✅	Cross-validated via Donchian equivalence
Dchannel	✅	Exact match—identical algorithm

Usage & Pitfalls

• Stale Extremes: Price Channel bands stay flat until a new extreme occurs or the old extreme exits the window. This is feature, not a bug.
• O(n) Trap: Naive implementations rescan the full window every bar. QuanTAlib's solution is O(1).
• Breakout vs. Touch: Price touching the upper band is not the same as breaking out. True breakouts close above/below the band.
• Asymmetric Exit: Consider different periods for long/short entries and exits (e.g., Turtle 20/10 rule).

API

classDiagram
    class Pchannel {
        +Name : string
        +WarmupPeriod : int
        +Upper : TValue
        +Lower : TValue
        +Last : TValue
        +IsHot : bool
        +Update(TBar bar) TValue
        +Update(TBarSeries source) TSeries
        +Prime(TBarSeries source) void
    }

Class: Pchannel

Parameter	Type	Default	Range	Description
period	int	—	>0	Lookback window size.
source	TBarSeries	—	any	Initial input source (optional).

Properties

• Name (string): The indicator name (e.g., "Pchannel(20)").
• WarmupPeriod (int): The number of samples needed for full validity.
• Upper (TValue): The current highest high.
• Lower (TValue): The current lowest low.
• Last (TValue): The current middle line value ((Upper + Lower) / 2).
• IsHot (bool): Returns true if we have processed period samples.

Methods

• Update(TBar bar): Updates the indicator with a new bar (High/Low) and returns the Middle band value.
• Update(TBarSeries source): Batch processes a series and returns (Middle, Upper, Lower) tuple.
• Prime(TBarSeries source): Pre-loads the indicator with history without returning results.

C# Example

using QuanTAlib;

// Initialize
var channel = new Pchannel(period: 20);

// Update Loop
foreach (var bar in bars)
{
    var result = channel.Update(bar);

    if (channel.IsHot)
    {
        Console.WriteLine($"{bar.Time}: Mid={result.Value:F2} Upper={channel.Upper.Value:F2} Lower={channel.Lower.Value:F2}");
    }
}

// Batch Processing
var (mid, upper, lower) = channel.Update(bars);

References

• Donchian, R. (1960). "High Finance in Copper." Financial Analysts Journal.
• Faith, C. (2007). Way of the Turtle: The Secret Methods that Turned Ordinary People into Legendary Traders.