mlfinlab.data_generation.bootstrap

Implementation of generating bootstrapped matrices from “Bootstrap validation of links of a minimum spanning tree” by F. Musciotto, L. Marotta, S. Miccichè, and R. N. Mantegna https://arxiv.org/pdf/1802.03395.pdf.

Module Contents

Functions

row_bootstrap(mat[, n_samples, size])

Uses the Row Bootstrap method to generate a new matrix of size equal or smaller than the given matrix.

pair_bootstrap(mat[, n_samples, size])

Uses the Pair Bootstrap method to generate a new correlation matrix of returns.

block_bootstrap(mat[, n_samples, size, block_size])

Uses the Block Bootstrap method to generate a new matrix of size equal to or smaller than the given matrix.
row_bootstrap(mat, n_samples=1, size=None)

Uses the Row Bootstrap method to generate a new matrix of size equal or smaller than the given matrix.

It samples with replacement a random row from the given matrix. If the required bootstrapped columns’ size is less than the columns of the original matrix, it randomly samples contiguous columns of the required size. It cannot generate a matrix greater than the original.

It is inspired by the following paper: Musciotto, F., Marotta, L., Miccichè, S. and Mantegna, R.N., 2018. Bootstrap validation of links of a minimum spanning tree. Physica A: Statistical Mechanics and its Applications, 512, pp.1032-1043..

Parameters:

  • mat – (pd.DataFrame/np.array) Matrix to sample from.

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

  • size – (tuple) Size of the bootstrapped matrix.

Returns:

(np.array) The generated bootstrapped matrices. Has shape (n_samples, size[0], size[1]).

pair_bootstrap(mat, n_samples=1, size=None)

Uses the Pair Bootstrap method to generate a new correlation matrix of returns.

It generates a correlation matrix based on the number of columns of the returns matrix given. It samples with replacement a pair of columns from the original matrix, the rows of the pairs generate a new row-bootstrapped matrix. The correlation value of the pair of assets is calculated and its value is used to fill the corresponding value in the generated correlation matrix.

It is inspired by the following paper: Musciotto, F., Marotta, L., Miccichè, S. and Mantegna, R.N., 2018. Bootstrap validation of links of a minimum spanning tree. Physica A: Statistical Mechanics and its Applications, 512, pp.1032-1043..

Parameters:

  • mat – (pd.DataFrame/np.array) Returns matrix to sample from.

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

  • size – (int) Size of the bootstrapped correlation matrix.

Returns:

(np.array) The generated bootstrapped correlation matrices. Has shape (n_samples, mat.shape[1], mat.shape[1]).

block_bootstrap(mat, n_samples=1, size=None, block_size=None)

Uses the Block Bootstrap method to generate a new matrix of size equal to or smaller than the given matrix.

It divides the original matrix into blocks of the given size. It samples with replacement random blocks to populate the bootstrapped matrix. It cannot generate a matrix greater than the original.

It is inspired by the following paper: Künsch, H.R., 1989. The jackknife and the bootstrap for general stationary observations. Annals of Statistics, 17(3), pp.1217-1241..

Parameters:

  • mat – (pd.DataFrame/np.array) Matrix to sample from.

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

  • size – (tuple) Size of the bootstrapped matrix.

  • block_size – (tuple) Size of the blocks.

Returns:

(np.array) The generated bootstrapped matrices. Has shape (n_samples, size[0], size[1]).