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.
4.2 KiB
EBSW: Ehlers Even Better Sinewave
EBSW is a refined cycle oscillator that combines a high-pass filter (trend removal), a Super-Smoother filter (noise removal), and Automatic Gain Control to produce a normalized [-1, +1] output representing the current position within the dominant market cycle. Developed by John Ehlers as an improvement over the original Hilbert Transform SineWave, it provides cleaner turning point detection without requiring complex phase extraction mathematics.
Historical Context
Ehlers' original SineWave indicator relied on the Hilbert Transform to extract phase, but direct Hilbert Transforms proved unstable on real market data due to amplitude sensitivity and convergence issues during strong trends. The "Even Better" SineWave, published in Cycle Analytics for Traders (2013), simplifies the approach: instead of complex phase math, it uses a tuned bandpass filter (high-pass cascaded with a 2-pole low-pass) to isolate the dominant cycle, then normalizes the result via RMS-based AGC. The 3-bar averaging in both the wave and power calculations acts as a simple anti-aliasing stage. The result is a more robust tool for identifying turning points in both trending and ranging markets.
Architecture & Physics
1. High-Pass Filter (Trend Removal)
A single-pole high-pass filter removes frequencies below the cutoff:
\alpha_1 = \frac{1 - \sin(2\pi / P_{HP})}{\cos(2\pi / P_{HP})}
HP_t = \frac{1 + \alpha_1}{2}(P_t - P_{t-1}) + \alpha_1 \cdot HP_{t-1}
2. Super-Smoother Filter (Noise Removal)
A 2-pole Butterworth low-pass attenuates high-frequency aliasing noise:
a = e^{-\sqrt{2}\pi / P_{SSF}}
b = 2a \cos(\sqrt{2}\pi / P_{SSF})
Filt_t = \frac{(1 - b + a^2)}{2}(HP_t + HP_{t-1}) + b \cdot Filt_{t-1} - a^2 \cdot Filt_{t-2}
3. Wave and Power Calculation
Three-bar averaging for both signal and energy:
Wave_t = \frac{Filt_t + Filt_{t-1} + Filt_{t-2}}{3}
Power_t = \frac{Filt_t^2 + Filt_{t-1}^2 + Filt_{t-2}^2}{3}
4. Normalization (AGC)
EBSW_t = \frac{Wave_t}{\sqrt{Power_t}}
Result is clamped to [-1, +1]. When Power \approx 0, output is zero.
5. Complexity
O(1) per bar. Fixed cascaded IIR filters with O(1) memory (only filter state variables and 3-bar history for wave/power).
Mathematical Foundation
Parameters
| Parameter | Description | Default | Constraint |
|---|---|---|---|
hpLength |
High-pass filter period (detrending cutoff) | 40 | \geq 1, \neq 4 |
ssfLength |
Super-smoother filter period (noise cutoff) | 10 | \geq 1 |
Precomputed Coefficients
α₁ = (1 - sin(2π/hpLength)) / cos(2π/hpLength)
a = exp(-√2·π / ssfLength)
b = 2·a·cos(√2·π / ssfLength)
c₁ = (1 - b + a²) / 2
Pseudo-code
function EBSW(source, hpLength, ssfLength):
// Precompute HP coefficient
α₁ ← (1 - sin(2π/hpLength)) / cos(2π/hpLength)
// Precompute SSF coefficients
a ← exp(-√2·π / ssfLength)
b ← 2·a·cos(√2·π / ssfLength)
c₁ ← (1 - b + a²) / 2
hp_prev ← 0; p_prev ← 0
filt_1 ← 0; filt_2 ← 0
for each price in source:
// High-pass filter
hp ← 0.5·(1 + α₁)·(price - p_prev) + α₁·hp_prev
// Super-smoother
filt ← c₁·(hp + hp_prev) + b·filt_1 - a²·filt_2
// Wave (3-bar average of filtered signal)
wave ← (filt + filt_1 + filt_2) / 3
// Power (3-bar RMS²)
power ← (filt² + filt_1² + filt_2²) / 3
// AGC normalization
ebsw ← (power > 0) ? wave / √power : 0
ebsw ← clamp(ebsw, -1, +1)
// Shift state
hp_prev ← hp; p_prev ← price
filt_2 ← filt_1; filt_1 ← filt
emit ebsw
Output Interpretation
| Condition | Meaning |
|---|---|
EBSW \approx +1 |
Cycle peak (potential short entry) |
EBSW \approx -1 |
Cycle trough (potential long entry) |
| Zero crossing up | Bullish phase transition |
| Zero crossing down | Bearish phase transition |
Railing at \pm 1 |
Strong directional move overwhelming cycle |
Resources
- Ehlers, J.F. Cycle Analytics for Traders. Wiley, 2013.
- Ehlers, J.F. Cybernetic Analysis for Stocks and Futures. Wiley, 2004.