A rich documentation is available in the GitHub repository.

heteroscedastic-edrvfl

Heteroscedastic ensemble deep random vector functional link neural network for high-frequency volatility forecasting and risk assessment.

heteroscedastic-edrvfl is a Python package for volatility forecasting using the HedRVFL model with multiple output layers.

HedRVFL combines randomized neural feature mapping, ensemble deep RVFL representations, heteroscedastic volatility information, and efficient regularized output-layer learning. This allows the model to capture nonlinear volatility dynamics with fast training.

Key Features

• HedRVFL Model: Implements a heteroscedastic ensemble deep RVFL model for high-frequency volatility forecasting and risk assessment.
• Multiple Output Layers: Uses layer-wise output readouts and aggregates predictions across hidden depths.
• Randomized Feature Learning: Uses randomly initialized hidden mappings with efficient output-layer training.
• Feature Selection: Includes feature-selection support to identify the most informative volatility predictors and reduce irrelevant input variables.
• Pruning Strategy: Uses pruning to remove weak or redundant hidden representations, improving model compactness and forecasting efficiency.
• Hyperparameter Tuning: Supports Hyperopt/TPE search for layer-wise model selection.
• Forecasting Metrics: Provides RMSE, MAE, NMAE, and Value-at-Risk helpers.

Installation

Downloading locally and installing:

git clone https://github.com/statsdl/heteroscedastic-edrvfl.git
cd heteroscedastic-edrvfl

Install dependencies:

pip install -r requirements.txt

Install the package:

pip install -e .

Using pip install from GitHub:

pip install git+https://github.com/statsdl/heteroscedastic-edrvfl.git

Using pip install from PyPI:

pip install heteroscedastic-edrvfl

Optional tuning installation:

pip install "heteroscedastic-edrvfl[tuning]"

Development installation:

pip install -e ".[dev]"

Usage

1. HedRVFLRegressor

from heteroscedastic_edrvfl import (
    HedRVFLRegressor,
    generate_synthetic_crypto_volatility,
    make_supervised_frame,
)

frame = generate_synthetic_crypto_volatility(n_steps=1200, seed=0)
X, y = make_supervised_frame(frame)

model = HedRVFLRegressor(n_layers=3, random_state=0)
model.fit(X[:800], y[:800])

pred = model.predict(X[800:])
print("Volatility forecasts:", pred[:5])

2. Hyperopt/TPE tuning

from heteroscedastic_edrvfl import generate_synthetic_crypto_volatility, make_supervised_frame
from heteroscedastic_edrvfl.tuning import tune_hedrvfl

frame = generate_synthetic_crypto_volatility(n_steps=1200, seed=0)
X, y = make_supervised_frame(frame)

result = tune_hedrvfl(
    X[:900],
    y[:900],
    n_layers=3,
    max_evals=10,
    random_state=0,
)

print("Best validation loss:", result.validation_loss)
print("Best parameters:", result.best_params)

The benchmark reports RMSE, MAE, NMAE, Value-at-Risk, tuning time, training time, testing time, and selected hyperparameters.

API Reference

HedRVFLRegressor

A heteroscedastic ensemble deep random vector functional link regressor for volatility forecasting.

Parameters

• n_layers (int): Number of stacked randomized hidden layers.
• layer_params (list): Optional layer-wise parameter dictionaries.
• random_state (int): Random seed for reproducibility.
• aggregation (str): Prediction aggregation method, either median or mean.

Methods

• fit(X, y): Fits the ensemble model.
• predict(X): Generates final volatility forecasts.
• predict(X, return_layers=True): Returns layer-wise predictions.

Tuning utilities

• hedrvfl_search_space: Returns the default Hyperopt/TPE search space.
• tune_hedrvfl: Tunes HedRVFL hyperparameters.

Metrics

• root_mean_squared_error: Computes RMSE.
• mean_absolute_error: Computes MAE.
• normalized_mean_absolute_error: Computes range-normalized MAE.
• value_at_risk: Computes normal Value-at-Risk from volatility forecasts.

License

This project is licensed under the MIT License. See the LICENSE file for details.

Citation

If you use this package in your research, please cite:

@article{bhambu2025heteroscedastic,
  title={Heteroscedastic ensemble deep random vector functional link neural network with multiple output layers for High Frequency Volatility Forecasting and Risk Assessment},
  author={Bhambu, Aryan and Suganthan, Ponnuthurai Nagaratnam and Natarajan, Selvaraju},
  journal={Neurocomputing},
  volume={638},
  pages={130078},
  year={2025},
  doi={10.1016/j.neucom.2025.130078}
}