SigmoidCycle Oscillator [LuminoAlgo]

Purpose:
The SineCycle Oscillator measures price momentum using sigmoid function mathematics (S-curve transformation) borrowed from neural network theory. It generates an oscillator that fluctuates around 1.0, identifying momentum shifts and potential reversal points.

Mathematical Foundation:
This indicator applies the sigmoid logistic function concept: y = 1/(1+e^-x), which creates an S-shaped curve. In financial markets context, this transformation:
- Maps price changes to a bounded range (-1 to +1)
- Provides non-linear sensitivity (high near zero, low at extremes)
- Naturally filters outliers without lag penalty

Calculation Process:

1. Statistical Normalization: Price deviations are measured from a moving average baseline and scaled by recent volatility (standard deviation over N periods)

2. Sigmoid Transformation: Normalized values undergo S-curve transformation, which weights small movements linearly but compresses large movements logarithmically

3. Dual Timeframe Analysis:
• Short window: User-defined period (N)
• Long window: Double period (2N)
• Ratio calculation: Short sigmoid average ÷ Long sigmoid average

4. Volatility-Weighted Smoothing: Final values use exponential smoothing where the smoothing factor adjusts based on the coefficient of variation (volatility/mean ratio)

What Makes This Different:
Unlike linear momentum oscillators (RSI, Stochastic) that use fixed mathematical relationships, the sigmoid transformation creates variable sensitivity zones. This mimics how professional traders mentally weight price movements.

Trading Application:

Signal Types:
- Momentum: Green (>1.0) = bullish, Red (<1.0) = bearish
- Reversals: 1.0 line crosses with volume confirmation
- Divergence: Price makes new high/low, oscillator doesn't
- Exhaustion: Extended readings (>1.2 or <0.8) suggest overextension

Optimal Conditions:
- Works best: Trending markets with clear swings
- Avoid: Low volume, ranging markets under 1% daily movement
- Timeframes: 4H and above for reliability

Parameter Guidelines:
- Length 8-10: Day trading (expect more whipsaws)
- Length 14-20: Swing trading (balanced signals)
- Length 25-30: Position trading (fewer, stronger signals)

Limitations:
- Lag increases with higher length settings
- Can give false signals during news-driven spikes
- Requires additional confirmation in choppy markets

Trading Framework:
Based on momentum persistence theory - assumes trends continue until sigmoid curve flattens (indicating momentum exhaustion). The mathematical model captures both mean reversion (extreme readings) and trend following (mid-range readings) characteristics.