BAHC

BAHC (Bootstrap Average Hierarchical Clustering) is a Python package for filtering covariance matrices using hierarchical clustering and bootstrap aggregation.

Installation

To install the package, you can use pip:

pip install bahc

Alternatively, you can clone the repository and install the dependencies manually:

git clone https://github.com/yourusername/bahc.git
cd bahc
pip install -r requirements.txt

Usage

Here is an example of how to use the BAHC class:

import numpy as np
from bahc import BAHC

# Generate random data
data = np.random.normal(0, 1, size=(10, 100))

# Create an instance of BAHC and filter the data
bahc_instance = BAHC(data, K=[1, 2, 3], Nboot=100, method='near', filter_type='correlation')

# Print the filtered matrix
print(bahc_instance.filter_matrix())

Methods

BAHC.__init__(self, data, K=1, Nboot=100, method='near', filter_type='covariance', seed=None)

Initializes the BAHC class and performs the filtering.

• data (ndarray): Data matrix (N x T).
• K (int or list): Recursion order.
• Nboot (int): Number of bootstraps.
• method (str): Regularization method ('no-neg' or 'near').
• filter_type (str): Type of filtering ('correlation' or 'covariance').
• seed (int): Random seed.

BAHC.filter_matrix(self)

Filters the matrix using k-BAHC.

• Returns: Filtered matrix (N x N). If K is a list, returns a list of matrices.

BAHC.nearest_positive_semidefinite(self, matrix, n_iter=100, eig_tol=1e-6, conv_tol=1e-8)

Finds the nearest positive semidefinite matrix.

• matrix (ndarray): Input matrix.
• n_iter (int): Maximum number of iterations.
• eig_tol (float): Eigenvalue tolerance.
• conv_tol (float): Convergence tolerance.
• Returns: Nearest positive semidefinite matrix.

BAHC._higher_order_covariance(self, C, K)

Computes higher order covariance matrices.

• C (ndarray): Input covariance matrix.
• K (list): List of recursion orders.
• Yields: Higher order covariance matrices.

BAHC._generate_noise(self, epsilon=1e-10)

Generates noise for the given dimensions.

• epsilon (float): Standard deviation of the noise.
• Returns: Generated noise matrix.

BAHC._remove_negative_eigenvalues(self, matrix)

Removes negative eigenvalues from the matrix.

• matrix (ndarray): Input matrix.
• Returns: Matrix with non-negative eigenvalues.

References

• Bongiorno, C., & Challet, D. (2021). Covariance matrix filtering with bootstrapped hierarchies. PLoS ONE, 16(1), e0245092.
• Bongiorno, C., & Challet, D. (2022). Reactive global minimum variance portfolios with k-BAHC covariance cleaning. The European Journal of Finance, 28(13-15), 1344-1360.

Please cite the above papers if you use this code.