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Miha Kralj
3eae9a76fe
- Implemented Sdchannel class for calculating standard deviation channels based on linear regression. - Added detailed documentation for SDCHANNEL, including overview, calculation methods, and interpretation. - Updated project files to include new numerics library components in Channels and Volatility projects.
156 lines
7.0 KiB
Markdown
156 lines
7.0 KiB
Markdown
# DC: Donchian Channels
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> "The Turtles didn't need complex math. They needed to know when price broke out of its cage."
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Donchian Channels (DC) track the highest high and lowest low over a lookback period, creating a price envelope that defines where the market has been. Unlike volatility-based bands (Bollinger, Keltner), Donchian 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.
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## Historical Context
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Richard Donchian developed these channels in the 1960s while managing one of the first publicly held commodity funds. His "4-week rule" (buy on 20-day high, sell on 20-day low) became the foundation for systematic trend-following.
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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 Donchian 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.
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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.
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## Architecture & Physics
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Donchian Channels consist of three components: upper band (highest high), lower band (lowest low), and middle band (their average).
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### 1. Upper Band (Highest High)
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Tracks the maximum high price over the lookback window:
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$$
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U_t = \max_{i=0}^{n-1}(H_{t-i})
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$$
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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.
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### 2. Lower Band (Lowest Low)
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Tracks the minimum low price over the lookback window:
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$$
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L_t = \min_{i=0}^{n-1}(L_{t-i})
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$$
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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.
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### 3. Middle Band
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The arithmetic mean of the upper and lower bands:
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$$
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M_t = \frac{U_t + L_t}{2}
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$$
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This represents the "equilibrium" price over the lookback period—not a moving average of closes, but the center of the price range.
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## Mathematical Foundation
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### Monotonic Deque Algorithm
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Instead of rescanning the window on each bar, the implementation maintains two monotonic deques:
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**For maximum (upper band):**
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1. Remove elements from the back that are smaller than the new value
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2. Add the new value with its index to the back
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3. Remove elements from the front whose indices are outside the window
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4. The front element is always the maximum
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**For minimum (lower band):**
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1. Remove elements from the back that are larger than the new value
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2. Add the new value with its index to the back
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3. Remove elements from the front whose indices are outside the window
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4. The front element is always the minimum
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**Amortized Analysis:**
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Each element is added once and removed at most once. Over $n$ operations, total work is $O(n)$, giving $O(1)$ amortized per update.
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### Channel Width
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The distance between bands measures price range volatility:
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$$
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W_t = U_t - L_t
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$$
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Wider channels indicate higher volatility; narrower channels suggest consolidation.
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## Performance Profile
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### Operation Count (Streaming Mode, Scalar)
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Per-bar cost using monotonic deque optimization:
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| CMP | 4 | 1 | 4 |
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| ADD | 1 | 1 | 1 |
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| MUL | 1 | 3 | 3 |
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| **Total** | **6** | — | **~8 cycles** |
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**Complexity**: O(1) amortized per bar—monotonic deque maintains max/min efficiently.
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### Batch Mode (512 values, SIMD/FMA)
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Finding max/min over sliding windows has limited SIMD benefit due to sequential dependency:
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| Operation | Scalar Ops | SIMD Benefit | Notes |
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| :--- | :---: | :---: | :--- |
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| Max/Min update | 4 | 1× | Deque-based, sequential |
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| Middle band | 2 | 2× | ADD + MUL parallelizable |
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**Batch efficiency (512 bars):**
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| Mode | Cycles/bar | Total (512 bars) | Improvement |
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| :--- | :---: | :---: | :---: |
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| Scalar streaming | 8 | 4,096 | — |
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| Partial SIMD | ~7 | ~3,584 | **~12%** |
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Donchian Channels are already highly efficient due to the O(1) monotonic deque algorithm.
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 10/10 | Exact max/min calculation |
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| **Timeliness** | 6/10 | Tracks past extremes, inherently lagging |
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| **Overshoot** | 10/10 | No overshoot—bands are actual price levels |
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| **Smoothness** | 5/10 | Bands move in discrete steps as extremes exit window |
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## Validation
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| Library | Status | Notes |
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| :--- | :---: | :--- |
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| **TA-Lib** | ✅ | Exact match for upper/lower bands |
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| **Skender** | ✅ | Exact match within floating-point tolerance |
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| **Tulip** | ✅ | Exact match |
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| **Ooples** | ✅ | Exact match |
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## Common Pitfalls
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1. **Stale Extremes**: Donchian bands stay flat until a new extreme occurs or the old extreme exits the window. A band that hasn't moved in 15 bars isn't broken—it's waiting. Traders sometimes mistake this for indicator malfunction.
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2. **O(n) Trap**: Naive implementations rescan the full window every bar. For period=200 on tick data (60,000 bars/day), that's 12 million comparisons daily per symbol. The monotonic deque approach reduces this to ~120,000.
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3. **Breakout vs. Touch**: Price touching the upper band is not the same as breaking out. True breakouts close above/below the band. Intrabar spikes that don't close outside the channel often fail.
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4. **Asymmetric Exit**: The Turtle system used 20-day entry but 10-day exit. Using the same period for both typically underperforms. Consider different periods for entries and exits.
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5. **Choppy Markets**: Donchian Channels generate frequent false signals during sideways consolidation. The bands narrow, making breakouts more likely, but these breakouts often fail. Filter with trend confirmation or volatility thresholds.
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6. **Gap Behavior**: Overnight gaps can create instant breakouts that reverse quickly. The band immediately adjusts to include the gap, which may not represent sustainable price levels.
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7. **Memory Footprint**: The monotonic deque implementation requires storing (value, index) pairs. For period=200, this means up to 400 doubles (3.2 KB) per instance. For 5,000 symbols, budget ~16 MB.
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## References
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- Donchian, R. (1960). "High Finance in Copper." *Financial Analysts Journal*, 16(6), 133-142.
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- Faith, C. (2007). *Way of the Turtle: The Secret Methods that Turned Ordinary People into Legendary Traders*. McGraw-Hill.
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- Schwager, J. D. (1989). *Market Wizards: Interviews with Top Traders*. Harper & Row.
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- Covel, M. (2007). *The Complete TurtleTrader*. HarperBusiness.
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