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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.
150 lines
7.4 KiB
Markdown
150 lines
7.4 KiB
Markdown
# MMCHANNEL: Min-Max Channel
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> "The market's true range isn't about averages. It's about extremes—and who's winning."
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Min-Max Channel (MMCHANNEL) tracks the highest high and lowest low over a lookback period, creating a pure price envelope without any midpoint calculation. Unlike Donchian Channels which include a middle band, MMCHANNEL delivers only the raw extremes—exactly what breakout traders and range analysis need. This implementation uses monotonic deques for O(1) amortized updates, making it suitable for high-frequency applications and long lookback periods.
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## Historical Context
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Min-Max channels represent the simplest form of price envelope analysis, predating most technical indicators. The concept is intuitive: track where price has been at its highest and lowest points over a defined period.
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The approach gained prominence through Richard Donchian's work in the 1960s and later through the Turtle Trading system. While Donchian Channels include a midpoint average, MMCHANNEL strips this away, focusing purely on support and resistance levels defined by actual price extremes.
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Most implementations suffer from O(n) complexity per update—scanning the entire window to find max/min values. For period=200 on tick data, this means 200 comparisons per tick. QuanTAlib uses monotonic deques that maintain sorted order implicitly, achieving O(1) amortized updates regardless of period length.
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## Architecture & Physics
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MMCHANNEL consists of two components: the upper band (highest high) and lower band (lowest low).
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### 1. Upper Band (Highest High)
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Tracks the maximum high price over the lookback window using a decreasing monotonic deque:
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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. New highs immediately update the upper band; the band only decreases when the previous maximum exits the lookback window.
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**Monotonic deque invariant:** Elements are stored in decreasing order by value. The front element is always the maximum.
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### 2. Lower Band (Lowest Low)
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Tracks the minimum low price over the lookback window using an increasing monotonic deque:
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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. New lows immediately update the lower band; the band only increases when the previous minimum exits the window.
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**Monotonic deque invariant:** Elements are stored in increasing order by value. The front element is always the minimum.
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## Mathematical Foundation
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### Monotonic Deque Algorithm
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The key insight is maintaining sorted order without explicit sorting:
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**For maximum (upper band):**
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1. **Back removal:** Remove elements from the back that are ≤ the new value
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2. **Insert:** Add the new (value, index) pair to the back
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3. **Front expiry:** Remove elements from the front whose indices are outside the window
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4. **Query:** The front element is always the maximum
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**For minimum (lower band):**
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1. **Back removal:** Remove elements from the back that are ≥ the new value
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2. **Insert:** Add the new (value, index) pair to the back
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3. **Front expiry:** Remove elements from the front whose indices are outside the window
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4. **Query:** The front element is always the minimum
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**Amortized Analysis:**
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Each element enters the deque exactly once and leaves at most once (either from the back during insertion or from the front during expiry). Over $n$ operations, total work is $O(n)$, yielding $O(1)$ amortized per update.
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### Channel Width
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The distance between bands measures the price range:
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$$
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W_t = U_t - L_t
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$$
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Channel width indicates volatility: wider channels suggest larger price swings; narrower channels indicate 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 (deque maintenance) | ~4 | 1 | ~4 |
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| Memory access (deque) | ~4 | 3 | ~12 |
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| **Total** | **~8** | — | **~16 cycles** |
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**Complexity:** O(1) amortized per bar. Worst case O(n) occurs only when a monotonically increasing (for max) or decreasing (for min) sequence forces clearing the entire deque—rare in practice.
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### Batch Mode (512 values, SIMD/FMA)
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Sliding window max/min has limited SIMD benefit due to sequential dependency in deque operations:
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| Operation | Scalar Ops | SIMD Benefit | Notes |
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| :--- | :---: | :---: | :--- |
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| Deque update | ~8 | 1× | Sequential by nature |
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| Index comparison | 2 | 2× | SIMD possible for batch |
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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 | 16 | 8,192 | — |
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| Partial SIMD | ~14 | ~7,168 | **~12%** |
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The monotonic deque algorithm is already highly efficient; SIMD provides marginal gains.
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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** | 4/10 | 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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| **Dchannel** | ✅ | Exact match for upper/lower bands |
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| **Skender** | ✅ | Exact match via Donchian upper/lower |
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| **TA-Lib** | ✅ | Exact match via MAX/MIN functions |
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| **Tulip** | ✅ | Exact match via max/min functions |
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## Common Pitfalls
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1. **Stale Extremes:** The 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 for price to exceed the current extreme or for that extreme to age out.
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2. **O(n) Implementation Trap:** Naive implementations rescan the window every bar. For period=200 on 60,000 bars/day, that's 12 million comparisons per symbol. The monotonic deque approach reduces this to ~120,000 operations.
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3. **Breakout vs. Touch:** Price touching the upper band differs from breaking out. True breakouts require closes above/below the band. Intrabar spikes that don't close outside the channel often reverse.
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4. **No Middle Band:** Unlike Donchian Channels, MMCHANNEL has no middle line. If you need a centerline, use Donchian or compute `(Upper + Lower) / 2` separately.
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5. **Asymmetric Movement:** Upper and lower bands move independently. The upper band can rise while the lower band stays flat (or vice versa) depending on where extremes occur in the lookback window.
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6. **Gap Handling:** Overnight gaps immediately adjust the relevant band. A gap up extends the upper band; a gap down extends the lower band. These may not represent sustainable price levels.
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7. **Memory Footprint:** The monotonic deque stores (value, index) pairs. Worst case is `2 * period` pairs per deque (monotonically decreasing high prices and monotonically increasing low prices). For period=200, budget ~6.4 KB per instance. For 5,000 symbols, ~32 MB total.
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8. **Bar Correction:** When `isNew=false`, the indicator must restore prior state before computing. The implementation maintains `_p_state` for this purpose. Failing to handle bar correction causes incorrect extremes when bars update intrabar.
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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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- Cormen, T. H., et al. (2009). *Introduction to Algorithms*, 3rd ed. MIT Press. (Monotonic deque analysis)
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