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.
3.0 KiB
CG: Ehlers Center of Gravity
CG identifies potential turning points using the physics concept of weighted center of mass applied to a price window. Developed by John Ehlers, the oscillator measures where the "weight" of prices is concentrated within a lookback period, producing a leading indicator that oscillates around zero with minimal lag compared to traditional moving average crossover systems.
Historical Context
John Ehlers introduced the Center of Gravity oscillator in Cybernetic Analysis for Stocks and Futures (2002). Drawing from classical mechanics, the indicator applies the concept that the center of mass of a distribution reveals its balance point. In the price context, the CG identifies where momentum is concentrated within a sliding window. Unlike momentum oscillators that differentiate price (and amplify noise), CG integrates position-weighted price, providing smoother turning point detection. The indicator's leading characteristic arises from the weighting scheme: as new prices shift the balance point, the CG responds before the window's simple average would.
Architecture & Physics
1. Weighted Sum (Numerator)
Position-weighted accumulation over the lookback window:
Num = \sum_{i=1}^{n} i \cdot P_{t-n+i}
where i ranges from 1 (oldest) to n (newest), giving linearly increasing weight to more recent data.
2. Simple Sum (Denominator)
Den = \sum_{i=1}^{n} P_{t-n+i}
3. Center of Gravity
CG_t = \frac{Num}{Den} - \frac{n + 1}{2}
The term \frac{n + 1}{2} is the geometric center of the window, centering the output around zero. When recent prices dominate, CG > 0 (bullish); when older prices dominate, CG < 0 (bearish).
4. Complexity
Streaming uses running sums for both numerator and denominator: O(1) per bar with O(n) memory for the ring buffer.
Mathematical Foundation
Parameters
| Parameter | Description | Default | Constraint |
|---|---|---|---|
period |
Lookback window length | 10 | > 0 |
Pseudo-code
function CG(source, period):
buffer ← RingBuffer(period)
runNum ← 0 // weighted sum
runDen ← 0 // simple sum
for each price in source:
buffer.Add(price)
if buffer.Count < period: continue
// Compute from buffer (or maintain running sums)
num = 0
den = 0
for i = 0 to period-1:
w = i + 1
num += w * buffer[i]
den += buffer[i]
cg = (den ≠ 0) ? (num / den) - (period + 1) / 2.0 : 0
emit cg
Output Interpretation
| Condition | Meaning |
|---|---|
CG > 0 |
Weight concentrated in recent prices (bullish momentum) |
CG < 0 |
Weight concentrated in older prices (bearish momentum) |
| Zero crossing up | Momentum shifting bullish |
| Zero crossing down | Momentum shifting bearish |
| Hanging at extremes | Strong trend in progress |
Resources
- Ehlers, J.F. Cybernetic Analysis for Stocks and Futures. Wiley, 2002.
- Ehlers, J.F. Rocket Science for Traders. Wiley, 2001.