mlfinlab.data_generation.vines

Implementation of generating financial correlation matrices from “Generating random correlation matrices based on vines and extended onion method” by Daniel Lewandowski, Dorota Kurowicka, Harry Joe. https://www.sciencedirect.com/science/article/pii/S0047259X09000876 and “Generating random correlation matrices based partial correlations” by Harry Joe. https://www.sciencedirect.com/science/article/pii/S0047259X05000886

Module Contents

Functions

sample_from_dvine([dim, n_samples, beta_dist_fixed])

Generates uniform correlation matrices using the D-vine method.

sample_from_cvine([dim, eta, n_samples, beta_dist_fixed])

Generates uniform correlation matrices using the C-vine method.

sample_from_ext_onion([dim, eta, n_samples])

Generates uniform correlation matrices using extended onion method.
sample_from_dvine(dim=10, n_samples=1, beta_dist_fixed=None)

Generates uniform correlation matrices using the D-vine method.

It is reproduced with modifications from the following paper: Joe, H., 2006. Generating random correlation matrices based on partial correlations. Journal of Multivariate Analysis, 97(10), pp.2177-2189.

It uses the partial correlation D-vine to generate partial correlations. The partial correlations are sampled from a uniform beta distribution and adjusted to thr range [-1, 1]. Then these partial correlations are converted into raw correlations by using a recursive formula based on its location on the vine.

Parameters:

  • dim – (int) Dimension of correlation matrix to generate.

  • n_samples – (int) Number of samples to generate.

  • beta_dist_fixed – (tuple) Overrides the beta distribution parameters. The input is two float parameters (alpha, beta), used in the distribution. (None by default)

Returns:

(np.array) Generated correlation matrices of shape (n_samples, dim, dim).

sample_from_cvine(dim=10, eta=2, n_samples=1, beta_dist_fixed=None)

Generates uniform correlation matrices using the C-vine method.

It is reproduced with modifications from the following paper: Lewandowski, D., Kurowicka, D. and Joe, H., 2009. Generating random correlation matrices based on vines and extended onion method. Journal of multivariate analysis, 100(9), pp.1989-2001.

It uses the partial correlation C-vine to generate partial correlations. The partial correlations are sampled from a uniform beta distribution proportional to its determinant and the factor eta. and adjusted to thr range [-1, 1]. Then these partial correlations are converted into raw correlations by using a recursive formula based on its location on the vine.

Parameters:

  • dim – (int) Dimension of correlation matrix to generate.

  • eta – (int) Corresponds to uniform distribution of beta. Correlation matrix S has a distribution proportional to [det C]^(eta - 1)

  • n_samples – (int) Number of samples to generate.

  • beta_dist_fixed – (tuple) Overrides the beta distribution parameters. The input is two float parameters (alpha, beta), used in the distribution. (None by default)

Returns:

(np.array) Generated correlation matrices of shape (n_samples, dim, dim).

sample_from_ext_onion(dim=10, eta=2, n_samples=1)

Generates uniform correlation matrices using extended onion method.

It is reproduced with modifications from the following paper: Lewandowski, D., Kurowicka, D. and Joe, H., 2009. Generating random correlation matrices based on vines and extended onion method. Journal of multivariate analysis, 100(9), pp.1989-2001.

It uses the extended onion to generate correlations sampled from a uniform beta distribution. It starts with a one-dimensional matrix, and it iteratively grows the matrix by adding extra rows and columns by sampling from the convex, closed, compact and full-dimensional set on the surface of a k-dimensional hypersphere.

Parameters:

  • dim – (int) Dimension of correlation matrix to generate.

  • eta – (int) Corresponds to uniform distribution of beta. Correlation matrix S has a distribution proportional to [det C]^(eta - 1)

  • n_samples – (int) Number of samples to generate.

Returns:

(np.array) Generated correlation matrices of shape (n_samples, dim, dim).