mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-04 12:07:44 +00:00
Miha Kralj
105 lines
4.4 KiB
Markdown
105 lines
4.4 KiB
Markdown
# DSP: Ehlers Detrended Synthetic Price
|
|
|
|
> *Detrended synthetic price removes the trend to expose the oscillation underneath — the signal beneath the drift.*
|
|
|
|
| Property | Value |
|
|
| ---------------- | -------------------------------- |
|
|
| **Category** | Cycle |
|
|
| **Inputs** | Source (close) |
|
|
| **Parameters** | `period` (default 40) |
|
|
| **Outputs** | Single series (Dsp) |
|
|
| **Output range** | Varies (see docs) |
|
|
| **Warmup** | `slowPeriod * 3` bars |
|
|
| **PineScript** | [dsp.pine](dsp.pine) |
|
|
|
|
- DSP creates a zero-centered oscillator by subtracting a half-cycle EMA from a quarter-cycle EMA, isolating the dominant cyclical component of price...
|
|
- **Similar:** [SSFDSP](../ssfdsp/Ssfdsp.md), [Ccyc](../ccyc/Ccyc.md) | **Complementary:** ATR for volatility filter | **Trading note:** Digital Signal Processing filter; separates signal from noise in price data.
|
|
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
|
|
|
|
DSP creates a zero-centered oscillator by subtracting a half-cycle EMA from a quarter-cycle EMA, isolating the dominant cyclical component of price while cancelling longer-term trends. Developed by John Ehlers, the indicator is grounded in cycle theory rather than arbitrary period selection, making it a principled alternative to MACD for cycle-aware trading. Bias-corrected EMAs ensure accurate amplitude during warmup.
|
|
|
|
## Historical Context
|
|
|
|
John Ehlers introduced the Detrended Synthetic Price as part of his cycle analytics framework. While MACD uses fixed periods (12/26), DSP calibrates its two EMAs to specific fractions of the dominant cycle period: quarter-cycle for the fast component and half-cycle for the slow. Subtracting aligned filters at these frequencies effectively bandpass-isolates the cycle of interest while suppressing both high-frequency noise and low-frequency trend. The "synthetic" label reflects that the output is a constructed signal that exposes cyclical energy invisible in raw price.
|
|
|
|
## Architecture & Physics
|
|
|
|
### 1. Component Periods
|
|
|
|
From the user-specified dominant cycle period $P$:
|
|
|
|
$$P_{fast} = \max(2, \lfloor P / 4 + 0.5 \rfloor)$$
|
|
|
|
$$P_{slow} = \max(3, \lfloor P / 2 + 0.5 \rfloor)$$
|
|
|
|
### 2. Alpha Coefficients
|
|
|
|
Standard EMA smoothing factors:
|
|
|
|
$$\alpha_{fast} = \frac{2}{P_{fast} + 1}, \qquad \alpha_{slow} = \frac{2}{P_{slow} + 1}$$
|
|
|
|
### 3. EMA Updates with Bias Correction
|
|
|
|
Raw EMA recursion:
|
|
|
|
$$EMA_{raw,t} = \alpha \cdot P_t + (1 - \alpha) \cdot EMA_{raw,t-1}$$
|
|
|
|
Warmup bias correction (prevents initial distortion):
|
|
|
|
$$EMA_t = \frac{EMA_{raw,t}}{1 - (1 - \alpha)^n}$$
|
|
|
|
where $n$ is the number of bars processed.
|
|
|
|
### 4. DSP Output
|
|
|
|
$$DSP_t = EMA_{fast,t} - EMA_{slow,t}$$
|
|
|
|
### 5. Complexity
|
|
|
|
$O(1)$ per bar with $O(1)$ memory. Two EMA state variables plus two bias correction accumulators.
|
|
|
|
## Mathematical Foundation
|
|
|
|
### Parameters
|
|
|
|
| Parameter | Description | Default | Constraint |
|
|
|-----------|-------------|---------|------------|
|
|
| `period` | Dominant cycle period | 40 | $\geq 4$ |
|
|
|
|
### Output Interpretation
|
|
|
|
| Condition | Meaning |
|
|
|-----------|---------|
|
|
| $DSP > 0$ | Fast EMA above slow: bullish cycle phase |
|
|
| $DSP < 0$ | Fast EMA below slow: bearish cycle phase |
|
|
| Zero crossing | Cycle phase transition point |
|
|
| Divergence from price | Cycle energy waning; potential trend exhaustion |
|
|
|
|
## Performance Profile
|
|
|
|
### Operation Count (Streaming Mode)
|
|
|
|
| Operation | Count | Cost (cycles) | Subtotal |
|
|
| :--- | :---: | :---: | :---: |
|
|
| ADD/SUB | 3 | 1 | 3 |
|
|
| MUL | 4 | 3 | 12 |
|
|
| FMA | 2 | 4 | 8 |
|
|
| DIV | 2 | 15 | 30 |
|
|
| **Total** | **11** | — | **~53 cycles** |
|
|
|
|
O(1) per bar. Two EMA updates (fast + slow) using FMA, plus warmup bias-correction divisions. After warmup completes, the DIV cost drops to zero, reducing steady-state to ~23 cycles.
|
|
|
|
### Quality Metrics
|
|
|
|
| Metric | Score | Notes |
|
|
| :--- | :---: | :--- |
|
|
| **Accuracy** | 9/10 | Bias-corrected EMAs eliminate warmup distortion |
|
|
| **Timeliness** | 8/10 | Quarter-cycle EMA responds quickly; half-cycle provides reference |
|
|
| **Smoothness** | 8/10 | Dual EMA differencing inherently smooths noise |
|
|
| **Memory** | 10/10 | O(1) state: 6 scalar values in record struct |
|
|
|
|
## Resources
|
|
|
|
- **Ehlers, J.F.** *Cybernetic Analysis for Stocks and Futures*. Wiley, 2004.
|
|
- **Ehlers, J.F.** *Rocket Science for Traders*. Wiley, 2001.
|