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153 lines
4.2 KiB
Markdown
153 lines
4.2 KiB
Markdown
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# HT_DCPHASE: Hilbert Transform - Dominant Cycle Phase
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> "The phase advances through a full 360-degree cycle as the dominant cycle completes; rapid phase changes indicate turning points."
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HT_DCPHASE measures the instantaneous phase angle of the dominant market cycle using Ehlers' Hilbert Transform cascade. The output ranges from -45° to 315°, with phase discontinuities marking cycle completions. This indicator times entries/exits based on cycle position.
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## Historical Context
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John Ehlers developed the Hilbert Transform cycle indicators in *Rocket Science for Traders* (2001). TA-Lib implements HT_DCPHASE directly from Ehlers' coefficients (A = 0.0962, B = 0.5769) with a 4-bar WMA prefilter and DC phase extraction from smoothed price history.
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QuanTAlib matches TA-Lib HT_DCPHASE output within floating-point tolerance.
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## Architecture & Physics
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The algorithm extracts phase from the complex analytic signal.
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### 1. WMA Price Smoothing
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$$
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SmoothPrice_t = \frac{4P_t + 3P_{t-1} + 2P_{t-2} + P_{t-3}}{10}
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$$
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### 2. Hilbert Transform Cascade
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- **Detrender (D)**: Removes DC component
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- **Quadrature (Q1)**: 90° phase-shifted version of D
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- **In-Phase (I1)**: D delayed by 3 bars
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- **jI, jQ**: Hilbert transforms of I1, Q1
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### 3. Phasor Components
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$$
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I2_t = I1_t - jQ_t
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$$
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$$
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Q2_t = Q1_t + jI_t
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$$
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Smoothed with EMA (α = 0.2).
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### 4. DC Phase Calculation
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Via DFT-like accumulation over smoothed period:
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$$
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DCPhase = \arctan\left(\frac{RealPart}{ImagPart}\right) \cdot \frac{180°}{\pi}
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$$
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Wrapped to range [-45°, 315°].
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## Performance Profile
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### Operation Count (Streaming Mode, per Bar)
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| MUL (Hilbert + DFT) | 45 | 3 | 135 |
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| SIN/COS (DFT loop) | 100 | 15 | 1500 |
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| ADD/SUB | 60 | 1 | 60 |
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| ATAN2 | 2 | 25 | 50 |
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| **Total** | **~207** | — | **~1745 cycles** |
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### Complexity Analysis
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- **Streaming:** O(P) per bar where P is smoothed period (~6-50)
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- **Memory:** ~1.2 KB per instance
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- **Warmup:** 63 bars (TA-Lib lookback)
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## Validation
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| Library | Status | Notes |
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| :--- | :---: | :--- |
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| TA-Lib | ✅ | Matches `TALib.Functions.HtDcPhase()` |
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| Skender | N/A | Not implemented |
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| PineScript | ✅ | Matches `ht_dcphase.pine` |
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## Usage & Pitfalls
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- **Phase range is -45° to 315°**—discontinuity at wrap is expected
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- **63-bar warmup required**—ignore early values
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- **Phase interpretation**:
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- -45° to 45°: Bottom / Start of uptrend
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- 45° to 135°: Rising / Mid-uptrend
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- 135° to 225°: Top / Start of downtrend
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- 225° to 315°: Falling / Mid-downtrend
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- **Do not smooth across discontinuity**—315° to -45° jump is cycle completion
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- **Strong trends** cause phase to advance slowly or get stuck
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- **Rapid phase change** often precedes price reversals
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## API
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```mermaid
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classDiagram
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class HtDcphase {
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+double Value
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+bool IsHot
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+HtDcphase()
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+HtDcphase(ITValuePublisher source)
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+TValue Update(TValue input, bool isNew)
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+void Reset()
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}
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```
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### Class: `HtDcphase`
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| Parameter | Type | Default | Range | Description |
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| :--- | :--- | :--- | :--- | :--- |
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| (none) | — | — | — | No constructor parameters |
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### Properties
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- `Value` (`double`): DC phase in degrees (-45° to 315°)
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- `IsHot` (`bool`): Returns `true` when warmup (63 bars) is complete
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### Methods
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- `Update(TValue input, bool isNew)`: Updates the indicator with a new data point
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## C# Example
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```csharp
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using QuanTAlib;
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// Create HT_DCPHASE
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var htPhase = new HtDcphase();
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// Update with streaming data
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foreach (var bar in quotes)
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{
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var result = htPhase.Update(new TValue(bar.Date, bar.Close));
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if (htPhase.IsHot)
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{
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double phase = result.Value;
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Console.WriteLine($"{bar.Date}: Phase = {phase:F1}°");
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// Cycle position detection
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if (phase >= -45 && phase < 45)
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Console.WriteLine(" → Cycle bottom zone");
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else if (phase >= 45 && phase < 135)
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Console.WriteLine(" → Rising phase");
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else if (phase >= 135 && phase < 225)
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Console.WriteLine(" → Cycle top zone");
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else
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Console.WriteLine(" → Falling phase");
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}
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}
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// Batch calculation
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var output = HtDcphase.Calculate(sourceSeries);
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```
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