mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-25 05:48:06 +00:00
Miha Kralj
d493bfd42f
- Updated Bessel, Bilateral, Blma, Butter, Conv, Ema, Kama, LSMA, MAMA, MGDI, SSF, USF, ATR, ADL, and ADOSC documentation to use bullet points for key concepts and features. - Added a new Qodana configuration file for code analysis. - Removed coverage configuration from Quantower.Tests.csproj to streamline testing setup.
139 lines
6.4 KiB
Markdown
139 lines
6.4 KiB
Markdown
# HT_SINE: Hilbert Transform - SineWave
|
||
|
||
[Pine Script Implementation of HT_SINE](https://github.com/mihakralj/pinescript/blob/main/indicators/cycles/ht_sine.pine)
|
||
|
||
## Overview and Purpose
|
||
|
||
The Hilbert Transform SineWave (HT_SINE) is a cycle visualization indicator developed by John Ehlers that generates sine and lead-sine wave plots based on the dominant market cycle identified through Hilbert Transform analysis. Unlike simple sine wave indicators that assume a fixed cycle period, HT_SINE adapts to the actual dominant cycle present in the market, providing a dynamic representation of cyclical behavior. The lead-sine component leads the sine wave, offering early signals of potential cycle turning points.
|
||
|
||
This indicator transforms the complex phase information from Hilbert Transform analysis into intuitive sine wave visualizations that oscillate between -1 and +1. By plotting both the sine wave (current cycle position) and lead-sine wave (advanced cycle position), traders can identify cycle peaks, troughs, and transitions. Crossovers between the sine and lead-sine waves often coincide with significant price turning points, making this a valuable tool for timing entries and exits in cyclical markets.
|
||
|
||
## Core Concepts
|
||
|
||
* **Sine Wave**: Visual representation of the dominant cycle position; oscillates smoothly between -1 and +1
|
||
* **Lead Sine Wave**: Phase-advanced version of sine wave; leads by delta_phase/period for early signals
|
||
* **Dynamic Phase**: Uses instantaneous phase from Hilbert Transform rather than fixed cycle assumption
|
||
* **Adaptive Cycle**: Automatically adjusts to dominant cycle period detected in price data
|
||
* **Crossover Signals**: Sine/LeadSine crossovers indicate potential cycle turning points
|
||
|
||
## Common Settings and Parameters
|
||
|
||
| Parameter | Default | Function | When to Adjust |
|
||
| ------ | ------ | ------ | ------ |
|
||
| Source | hlc3 | Price data for cycle analysis | Use close for simpler signals; hlc3 for smoother, more comprehensive cycle detection |
|
||
|
||
**Pro Tip:** Watch for crossovers between the sine and lead-sine waves as potential cycle reversal signals. When lead-sine crosses above sine near the trough (-1), it suggests an upcoming cycle bottom. When lead-sine crosses below sine near the peak (+1), it suggests an upcoming cycle top. The indicator works best in ranging or cyclical markets; strong trends can produce less reliable signals as the cycle assumption breaks down.
|
||
|
||
## Calculation and Mathematical Foundation
|
||
|
||
**Simplified explanation:**
|
||
HT_SINE uses Hilbert Transform to determine the dominant cycle's phase, then generates sine and lead-sine waves based on that phase for visual cycle representation.
|
||
|
||
**Technical formula:**
|
||
|
||
1. Smooth the price data:
|
||
```
|
||
SmoothPrice = (4×Price + 3×Price[1] + 2×Price[2] + Price[3]) / 10
|
||
```
|
||
|
||
2. Detrend with adaptive bandwidth:
|
||
```
|
||
Bandwidth = 0.075 × Period[1] + 0.54
|
||
Detrender = Hilbert_FIR(SmoothPrice) × Bandwidth
|
||
```
|
||
|
||
3. Calculate Quadrature and In-phase components:
|
||
```
|
||
Q1 = Hilbert_FIR(Detrender) × Bandwidth
|
||
I1 = Detrender[3]
|
||
```
|
||
|
||
4. Apply Hilbert Transform:
|
||
```
|
||
jI = Hilbert_FIR(I1) × Bandwidth
|
||
jQ = Hilbert_FIR(Q1) × Bandwidth
|
||
```
|
||
|
||
5. Compute smoothed I2 and Q2:
|
||
```
|
||
I2 = I1 - jQ
|
||
Q2 = Q1 + jI
|
||
I2 = 0.2×I2 + 0.8×I2[1]
|
||
Q2 = 0.2×Q2 + 0.8×Q2[1]
|
||
```
|
||
|
||
6. Calculate phase using four-quadrant arctangent:
|
||
```
|
||
if I2 > 0:
|
||
Phase = atan(Q2 / I2)
|
||
else if I2 < 0:
|
||
Phase = atan(Q2 / I2) ± π
|
||
else:
|
||
Phase = ±π/2
|
||
```
|
||
|
||
7. Compute phase change and alpha:
|
||
```
|
||
DeltaPhase = max(Phase[1] - Phase, 1.0)
|
||
Alpha = DeltaPhase / Period
|
||
```
|
||
|
||
8. Generate sine waves:
|
||
```
|
||
Sine = sin(Phase)
|
||
LeadSine = sin(Phase + Alpha)
|
||
```
|
||
|
||
Where `Hilbert_FIR` is a finite impulse response filter with coefficients [0.0962, 0.5769, 0, -0.5769, -0.0962].
|
||
|
||
> 🔍 **Technical Note:** The lead-sine component is phase-advanced by alpha (DeltaPhase/Period), causing it to lead the sine wave. The minimum DeltaPhase constraint of 1.0 prevents division issues when phase changes slowly. The sine waves are bounded between -1 and +1, providing normalized cycle visualization regardless of price magnitude.
|
||
|
||
## Interpretation Details
|
||
|
||
HT_SINE provides cycle visualization and timing signals through multiple perspectives:
|
||
|
||
* **Wave Position:**
|
||
* Sine ≈ +1: Cycle peak (potential sell zone)
|
||
* Sine ≈ 0: Mid-cycle (transition zone)
|
||
* Sine ≈ -1: Cycle trough (potential buy zone)
|
||
* Regular oscillation indicates clean cyclical behavior
|
||
|
||
* **Crossover Signals:**
|
||
* LeadSine crosses above Sine: Potential bullish reversal signal
|
||
* LeadSine crosses below Sine: Potential bearish reversal signal
|
||
* Crossovers near extremes (+1 or -1) are most reliable
|
||
* Multiple rapid crossovers suggest choppy, non-cyclical conditions
|
||
|
||
* **Wave Separation:**
|
||
* Wide separation: Strong, clear cycle in progress
|
||
* Narrow separation: Weak or transitioning cycle
|
||
* Consistent spacing: Steady cycle frequency
|
||
* Erratic spacing: Cycle instability or trend dominance
|
||
|
||
* **Extreme Levels:**
|
||
* Both waves at +1: Confirmed cycle peak
|
||
* Both waves at -1: Confirmed cycle trough
|
||
* Failure to reach extremes: Weakening cycle or trend emergence
|
||
* Extended time at extremes: Possible trend rather than cycle
|
||
|
||
* **Lead-Lag Relationship:**
|
||
* Lead-sine consistently ahead: Normal cycle mode
|
||
* Lead-sine loses leadership: Cycle breaking down
|
||
* Waves synchronizing: Transitioning to trend mode
|
||
* Lead reversing direction first: Early warning signal
|
||
|
||
## Limitations and Considerations
|
||
|
||
* **Cycle Assumption:** Assumes market is in cyclical mode; less reliable during strong trends
|
||
* **Lag Component:** Despite "lead-sine," overall indicator lags actual price action due to Hilbert Transform smoothing
|
||
* **False Signals:** Can generate whipsaws in choppy, non-cyclical markets
|
||
* **Trend Weakness:** Strong directional moves violate cycle assumptions, producing unreliable waves
|
||
* **Period Dependency:** Relies on accurate dominant cycle detection; errors in period affect wave quality
|
||
* **Visual Tool:** Best used as confirmation with other indicators rather than standalone timing tool
|
||
|
||
## References
|
||
|
||
* Ehlers, J. F. (2004). "Cybernetic Analysis for Stocks and Futures." John Wiley & Sons.
|
||
* Ehlers, J. F. (2001). "Rocket Science for Traders: Digital Signal Processing Applications." John Wiley & Sons.
|
||
* Ehlers, J. F. (2013). "Cycle Analytics for Traders: Advanced Technical Trading Concepts." John Wiley & Sons.
|