Merge branch 'main' with resolved conflicts

docs/analysis.md

@@ -14,6 +14,19 @@ The `Analysis` module includes classes for calculating common technical indicato
 Found in `cycles/Analysis/rsi.py`.
 
 Calculates the Relative Strength Index.
+### Mathematical Model  
+1. **Average Gain (AvgU)** and **Average Loss (AvgD)** over 14 periods:  
+   $$
+   \text{AvgU} = \frac{\sum \text{Upward Price Changes}}{14}, \quad \text{AvgD} = \frac{\sum \text{Downward Price Changes}}{14}
+   $$  
+2. **Relative Strength (RS)**:  
+   $$
+   RS = \frac{\text{AvgU}}{\text{AvgD}}
+   $$  
+3. **RSI**:  
+   $$
+   RSI = 100 - \frac{100}{1 + RS}
+   $$  
 
 ### `__init__(self, period: int = 14)`
 
@@ -33,7 +46,21 @@ Calculates the Relative Strength Index.
 
 Found in `cycles/Analysis/boillinger_band.py`.
 
-Calculates Bollinger Bands for given financial data.
+## **Bollinger Bands**  
+### Mathematical Model  
+1. **Middle Band**: 20-day Simple Moving Average (SMA)  
+   $$
+   \text{Middle Band} = \frac{1}{20} \sum_{i=1}^{20} \text{Close}_{t-i}
+   $$  
+2. **Upper Band**: Middle Band + 2 × 20-day Standard Deviation (σ)  
+   $$
+   \text{Upper Band} = \text{Middle Band} + 2 \times \sigma_{20}
+   $$  
+3. **Lower Band**: Middle Band − 2 × 20-day Standard Deviation (σ)  
+   $$
+   \text{Lower Band} = \text{Middle Band} - 2 \times \sigma_{20}
+   $$  
+
 
 ### `__init__(self, period: int = 20, std_dev_multiplier: float = 2.0)`