mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-16 09:38:05 +00:00
Miha Kralj
26280ce80b
- Implemented ChopIndicator for Quantower with configurable period and cold value display. - Created Chop class for calculating the Choppiness Index with detailed documentation. - Added comprehensive unit tests for Chop functionality, covering various market conditions and edge cases. - Developed markdown documentation for CHOP, detailing its historical context, mathematical foundation, and usage examples. - Established a remediation plan for channel indicators documentation, identifying gaps and prioritizing updates.
153 lines
4.2 KiB
Markdown
153 lines
4.2 KiB
Markdown
# HT_DCPHASE: Hilbert Transform - Dominant Cycle Phase
|
||
|
||
> "The phase advances through a full 360-degree cycle as the dominant cycle completes; rapid phase changes indicate turning points."
|
||
|
||
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.
|
||
|
||
## Historical Context
|
||
|
||
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.
|
||
|
||
QuanTAlib matches TA-Lib HT_DCPHASE output within floating-point tolerance.
|
||
|
||
## Architecture & Physics
|
||
|
||
The algorithm extracts phase from the complex analytic signal.
|
||
|
||
### 1. WMA Price Smoothing
|
||
|
||
$$
|
||
SmoothPrice_t = \frac{4P_t + 3P_{t-1} + 2P_{t-2} + P_{t-3}}{10}
|
||
$$
|
||
|
||
### 2. Hilbert Transform Cascade
|
||
|
||
- **Detrender (D)**: Removes DC component
|
||
- **Quadrature (Q1)**: 90° phase-shifted version of D
|
||
- **In-Phase (I1)**: D delayed by 3 bars
|
||
- **jI, jQ**: Hilbert transforms of I1, Q1
|
||
|
||
### 3. Phasor Components
|
||
|
||
$$
|
||
I2_t = I1_t - jQ_t
|
||
$$
|
||
|
||
$$
|
||
Q2_t = Q1_t + jI_t
|
||
$$
|
||
|
||
Smoothed with EMA (α = 0.2).
|
||
|
||
### 4. DC Phase Calculation
|
||
|
||
Via DFT-like accumulation over smoothed period:
|
||
|
||
$$
|
||
DCPhase = \arctan\left(\frac{RealPart}{ImagPart}\right) \cdot \frac{180°}{\pi}
|
||
$$
|
||
|
||
Wrapped to range [-45°, 315°].
|
||
|
||
## Performance Profile
|
||
|
||
### Operation Count (Streaming Mode, per Bar)
|
||
|
||
| Operation | Count | Cost (cycles) | Subtotal |
|
||
| :--- | :---: | :---: | :---: |
|
||
| MUL (Hilbert + DFT) | 45 | 3 | 135 |
|
||
| SIN/COS (DFT loop) | 100 | 15 | 1500 |
|
||
| ADD/SUB | 60 | 1 | 60 |
|
||
| ATAN2 | 2 | 25 | 50 |
|
||
| **Total** | **~207** | — | **~1745 cycles** |
|
||
|
||
### Complexity Analysis
|
||
|
||
- **Streaming:** O(P) per bar where P is smoothed period (~6-50)
|
||
- **Memory:** ~1.2 KB per instance
|
||
- **Warmup:** 63 bars (TA-Lib lookback)
|
||
|
||
## Validation
|
||
|
||
| Library | Status | Notes |
|
||
| :--- | :---: | :--- |
|
||
| TA-Lib | ✅ | Matches `TALib.Functions.HtDcPhase()` |
|
||
| Skender | N/A | Not implemented |
|
||
| PineScript | ✅ | Matches `ht_dcphase.pine` |
|
||
|
||
## Usage & Pitfalls
|
||
|
||
- **Phase range is -45° to 315°**—discontinuity at wrap is expected
|
||
- **63-bar warmup required**—ignore early values
|
||
- **Phase interpretation**:
|
||
- -45° to 45°: Bottom / Start of uptrend
|
||
- 45° to 135°: Rising / Mid-uptrend
|
||
- 135° to 225°: Top / Start of downtrend
|
||
- 225° to 315°: Falling / Mid-downtrend
|
||
- **Do not smooth across discontinuity**—315° to -45° jump is cycle completion
|
||
- **Strong trends** cause phase to advance slowly or get stuck
|
||
- **Rapid phase change** often precedes price reversals
|
||
|
||
## API
|
||
|
||
```mermaid
|
||
classDiagram
|
||
class HtDcphase {
|
||
+double Value
|
||
+bool IsHot
|
||
+HtDcphase()
|
||
+HtDcphase(ITValuePublisher source)
|
||
+TValue Update(TValue input, bool isNew)
|
||
+void Reset()
|
||
}
|
||
```
|
||
|
||
### Class: `HtDcphase`
|
||
|
||
| Parameter | Type | Default | Range | Description |
|
||
| :--- | :--- | :--- | :--- | :--- |
|
||
| (none) | — | — | — | No constructor parameters |
|
||
|
||
### Properties
|
||
|
||
- `Value` (`double`): DC phase in degrees (-45° to 315°)
|
||
- `IsHot` (`bool`): Returns `true` when warmup (63 bars) is complete
|
||
|
||
### Methods
|
||
|
||
- `Update(TValue input, bool isNew)`: Updates the indicator with a new data point
|
||
|
||
## C# Example
|
||
|
||
```csharp
|
||
using QuanTAlib;
|
||
|
||
// Create HT_DCPHASE
|
||
var htPhase = new HtDcphase();
|
||
|
||
// Update with streaming data
|
||
foreach (var bar in quotes)
|
||
{
|
||
var result = htPhase.Update(new TValue(bar.Date, bar.Close));
|
||
|
||
if (htPhase.IsHot)
|
||
{
|
||
double phase = result.Value;
|
||
Console.WriteLine($"{bar.Date}: Phase = {phase:F1}°");
|
||
|
||
// Cycle position detection
|
||
if (phase >= -45 && phase < 45)
|
||
Console.WriteLine(" → Cycle bottom zone");
|
||
else if (phase >= 45 && phase < 135)
|
||
Console.WriteLine(" → Rising phase");
|
||
else if (phase >= 135 && phase < 225)
|
||
Console.WriteLine(" → Cycle top zone");
|
||
else
|
||
Console.WriteLine(" → Falling phase");
|
||
}
|
||
}
|
||
|
||
// Batch calculation
|
||
var output = HtDcphase.Calculate(sourceSeries);
|
||
```
|