Miha Kralj
90d5638008
- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
3.2 KiB
DSP: Ehlers Detrended Synthetic Price
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 |
Pseudo-code
function DSP(source, period):
pFast ← max(2, round(period / 4))
pSlow ← max(3, round(period / 2))
αFast ← 2 / (pFast + 1)
αSlow ← 2 / (pSlow + 1)
emaFastRaw ← 0
emaSlowRaw ← 0
decayFast ← 1.0 // (1 - αFast)^n
decaySlow ← 1.0 // (1 - αSlow)^n
for each price in source:
emaFastRaw ← FMA(αFast, price, (1 - αFast) * emaFastRaw)
emaSlowRaw ← FMA(αSlow, price, (1 - αSlow) * emaSlowRaw)
decayFast *= (1 - αFast)
decaySlow *= (1 - αSlow)
emaFast ← emaFastRaw / (1 - decayFast)
emaSlow ← emaSlowRaw / (1 - decaySlow)
dsp ← emaFast - emaSlow
emit dsp
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 |
Resources
- Ehlers, J.F. Cybernetic Analysis for Stocks and Futures. Wiley, 2004.
- Ehlers, J.F. Rocket Science for Traders. Wiley, 2001.