# SSM-FastICANet : A Hybrid State Space and FastICA Model for Economic Growth Forecasting in Energy Economy-Environment Systems

## Overview
SSM-FastICANet is a novel hybrid model that integrates State Space Models (SSM) with Independent Component Analysis (FastICA) to enhance economic growth forecasting in Energy-Economy-Environment (3E) systems. The model effectively captures complex interactions between CO2 emissions, economic growth, and energy consumption, providing accurate forecasts and valuable insights for sustainable development policies.

## Dataset Information
- **Data Source**: The model uses time-series data from 1971-2019 for China, covering:
  - Renewable energy consumption (REC)
  - Non-renewable energy consumption (NREC)
  - CO2 emissions
  - GDP per capita
- **Data Preprocessing**: 
  - Normalization using Min-Max scaling
  - Train-validation-test split (80%-10%-10%)
  - Sequence generation with a lookback window of 5 time steps

## Code Information
The implementation is contained in a single Jupyter notebook with the following components:

### Prerequisites
Library	 Version
Python	3.8.18
PyTorch	2.2.2
NumPy	  1.26.4
Pandas  2.2.2
Scikit-learn	1.4.2
Matplotlib	3.8.4
SciPy	1.13.0

### Model Architecture
The SSM-FastICANet model consists of:
1. **FastICA Component**: Extracts independent components from input data
2. **State Space Model**: Implements a diagonal state transition matrix
3. **Dynamic Initialization**: Uses statistical measures (kurtosis, skewness, entropy) to filter components

## Usage Instructions
1. **Environment Setup**:
   ```bash
   # Create and activate a Python environment
   conda create -n ssm-fastica python=3.8
   conda activate ssm-fastica

   # Install required packages
   pip install torch numpy pandas scikit-learn matplotlib scipy
   ```

2. **Data Preparation**:
   - Place your dataset (Excel format) in the same directory as the notebook
   - The dataset should contain columns for Year, REC, NREC, CO2, and GDP

3. **Running the Model**:
   - Open the Jupyter notebook
   - Execute cells sequentially
   - The model will automatically:
     - Load and preprocess the data # ensure that code and dataset file in the same folder 
     - Create sequences for time-series forecasting
     - Initialize and train the SSM-FastICANet model
     - Evaluate performance and display results

## Computing Infrastructure
- **Hardware Used**: 
  - CPU: Intel Core i7 or equivalent
  - RAM: 26GB
  - GPU: Not required but can accelerate training
- **Software Environment**:
  - Operating System: Windows 11
  - Python Environment: Miniconda
  - VSCode Notebook

## Methodology
The SSM-FastICANet methodology follows these key steps:

1. **Data Preprocessing**:
   - Normalize variables (renewable and non-renewable energy, CO₂ emissions, GDP)
   - Create time-series sequences with a lookback window of 5 years

2. **FastICA for Pattern Recognition**:
   - Extract independent components (ICs) that represent distinct underlying processes
   - Identify non-Gaussian patterns in energy consumption and emissions data

3. **Component Filtering**:
   - Calculate kurtosis (retain ICs with higher kurtosis)
   - Measure skewness (retain ICs with higher skewness)
   - Compute entropy (discard ICs with higher entropy)

4. **State Space Model Initialization**:
   - Initialize diagonal state transition matrix (A)
   - Create input-to-state matrix (B)
   - Establish state-to-output matrix (C)
   - Set up input-to-output matrix (D)

5. **Model Training and Evaluation**:
   - Train using MSE loss function
   - Validate on a separate dataset
   - Test final performance using RMSE, MAE, and R² metrics

## Results
The SSM-FastICANet model demonstrates superior performance compared to baseline models:

- Achieves lower test loss compared to traditional models
- Shows rapid convergence during training
- Demonstrates superior performance in:
  - Mean Absolute Error (MAE)
  - Root Mean Squared Error (RMSE)
  - R-squared (R²)

The model effectively captures the complex relationships between energy consumption, CO2 emissions, and economic growth, providing valuable insights for policymakers.

## Limitations and Challenges
- **Convergence Issues**: FastICA occasionally fails to converge, requiring parameter adjustments
- **Data Limitations**: Limited historical data available for some regions
- **Hyperparameter Sensitivity**: Model performance depends on careful selection of:
  - Number of components
  - Hidden dimension size
  - Learning rate

## Future Work
- Improve FastICA convergence through advanced initialization techniques
- Extend the model to incorporate additional variables (technological innovation, policy changes)
- Develop a multi-regional version for comparative analysis
- Implement ensemble methods to further improve forecast accuracy
- Create a more user-friendly interface for non-technical stakeholders

## Citation
If you use SSM-FastICANet in your research, please cite our paper:
```
@article{SSMFastICANet2023,
  title={SSM-FastICANet : A Hybrid State Space and FastICA Model for Economic Growth Forecasting in Energy Economy-Environment Systems},
  author={[Fahman Saeed]},
  journal={[Peerj]},
  year={2025},
  volume={},
  pages={}
}
```

## Acknowledgments
This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) (grant number IMSIU-DDRSP2503).