FEATURES.md

# Features Overview

<!--
Author: RSK World
Website: https://rskworld.in
Email: help@rskworld.in
Phone: +91 93305 39277
-->

## Complete Feature List

### 1. Regression Analysis (`regression_analysis.py`)
- **Linear Regression (OLS)**
- Model fitting with intercept option
- Prediction on new data
- Residual analysis
- Fitted values extraction

- **Generalized Linear Models (GLM)**
- Multiple family support (Gaussian, Binomial, Poisson, etc.)
- Flexible link functions
- Model summary and diagnostics

- **Diagnostic Tools**
- Residual plots (vs fitted, Q-Q, histogram, scale-location)
- Multicollinearity check (VIF)
- Heteroscedasticity test (Breusch-Pagan)
- Autocorrelation test (Durbin-Watson)

### 2. Time Series Analysis (`time_series_analysis.py`)
- **ARIMA Models**
- ARIMA(p,d,q) fitting
- Model summary and diagnostics
- Forecasting with confidence intervals

- **Time Series Decomposition**
- Additive and multiplicative decomposition
- Trend, seasonal, and residual components
- Visualization of components

- **Stationarity Testing**
- Augmented Dickey-Fuller (ADF) test
- Results interpretation

- **ACF/PACF Analysis**
- Autocorrelation function plots
- Partial autocorrelation function plots
- Lag selection guidance

- **Exponential Smoothing**
- Holt-Winters exponential smoothing
- Trend and seasonal components
- Multiple smoothing methods

- **Vector Autoregression (VAR)**
- Multivariate time series modeling
- Lag order selection
- Forecasting multiple series

### 3. Advanced Time Series (`advanced_time_series.py`)
- **SARIMA Models**
- Seasonal ARIMA fitting
- Seasonal order specification
- Enhanced forecasting capabilities

- **Auto ARIMA Selection**
- Automatic order selection
- AIC-based model comparison
- Seasonal component detection
- Comprehensive search algorithm

- **Comprehensive Stationarity Tests**
- ADF test
- KPSS test
- Combined test results
- Detailed interpretation

### 4. Hypothesis Testing (`hypothesis_testing.py`)
- **Parametric Tests**
- One-sample t-test
- Two-sample t-test
- Z-test (one and two sample)
- ANOVA (one-way)
- Chi-square test
- Proportion tests

- **Non-Parametric Tests**
- Mann-Whitney U test
- Kruskal-Wallis test
- Normality tests (Shapiro-Wilk, Jarque-Bera, Lilliefors)

- **Normality Testing**
- Multiple test methods
- Q-Q plots
- Histogram with normal overlay
- Comprehensive results

### 5. Statistical Diagnostics (`statistical_diagnostics.py`)
- **Comprehensive Diagnostics**
- Linearity test (Rainbow test)
- Heteroscedasticity tests (Breusch-Pagan, White)
- Autocorrelation tests (Durbin-Watson, Ljung-Box)
- Multicollinearity (VIF)
- Normality of residuals
- Influential points (Cook's distance)

- **Diagnostic Plots**
- Residuals vs fitted
- Q-Q plots
- Scale-location plots
- Leverage plots
- ACF of residuals

### 6. Econometric Modeling (`econometric_modeling.py`)
- **Vector Autoregression (VAR)**
- Multivariate time series modeling
- Optimal lag selection (AIC, BIC, FPE, HQIC)
- Model summary and diagnostics

- **VARMAX Models**
- VAR with moving average component
- Enhanced forecasting
- Model comparison

- **Cointegration Tests**
- Johansen cointegration test
- Engle-Granger test
- Cointegrating vector estimation

- **Impulse Response Functions**
- IRF calculation
- Orthogonalized IRF
- Visualization of responses

- **Forecast Error Variance Decomposition**
- FEVD calculation
- Variance contribution analysis
- Visualization

- **Granger Causality**
- Causality testing
- F-test implementation
- Results interpretation

### 7. Model Selection (`model_selection.py`)
- **Model Comparison**
- Multiple model comparison
- AIC, BIC, R² comparison
- F-statistic comparison
- Log-likelihood comparison

- **Stepwise Selection**
- Forward selection
- Backward elimination
- Combined stepwise
- P-value thresholds

- **Information Criteria**
- AIC calculation
- BIC calculation
- HQIC calculation
- Comparison plots

- **Feature Selection**
- VIF-based feature removal
- Correlation filtering
- Automated feature selection

### 8. Model Evaluation (`model_evaluation.py`)
- **Cross-Validation**
- K-fold cross-validation
- Time series cross-validation
- Multiple scoring metrics (MSE, MAE, R²)

- **Evaluation Metrics**
- Mean Squared Error (MSE)
- Root Mean Squared Error (RMSE)
- Mean Absolute Error (MAE)
- R-squared (R²)
- Mean Absolute Percentage Error (MAPE)

- **Visualization**
- Actual vs predicted plots
- Residual plots
- Learning curves

### 9. Data Preprocessing (`data_preprocessing.py`)
- **Missing Value Handling**
- Mean imputation
- Median imputation
- Mode imputation
- Forward fill
- Drop missing values

- **Outlier Detection**
- IQR method
- Z-score method
- Outlier removal

- **Data Scaling**
- Standard scaling
- Min-max scaling
- Robust scaling

- **Time Series Transformations**
- Differencing
- Log differencing
- Detrending

- **Feature Engineering**
- Lag creation
- Rolling window features
- Summary statistics

### 10. Visualization Utilities (`visualization_utils.py`)
- **Correlation Analysis**
- Correlation matrix heatmap
- Customizable colormaps

- **Distribution Plots**
- Histograms with KDE
- Distribution comparison

- **Time Series Plots**
- Single time series
- Multiple time series
- Forecast comparison

- **Residual Analysis**
- Comprehensive residual plots
- Q-Q plots
- Scale-location plots

- **Model Comparison**
- Bar charts for metrics
- Model ranking visualization

- **Feature Importance**
- Coefficient plots
- Importance ranking

- **Learning Curves**
- Training/validation curves
- Overfitting detection

## Usage Examples

All features are demonstrated in:
- Jupyter notebooks in `notebooks/` directory
- Example scripts in `examples/` directory
- Comprehensive documentation in README.md

## Author

**RSK World**
- Website: https://rskworld.in
- Email: help@rskworld.in
- Phone: +91 93305 39277