Core

Statistical primitives: EWMA, returns, moments, correlation/covariance matrices, and linear algebra.

core

correlation_matrix

correlation_matrix(data)

Pearson correlation matrix.

Parameters:

Name	Type	Description	Default
data	ndarray	2-D array of shape (n_observations, n_variables).	required

Returns:

Type	Description
ndarray	Symmetric correlation matrix of shape (n_variables, n_variables).

covariance_matrix

covariance_matrix(data)

Sample covariance matrix.

Parameters:

Name	Type	Description	Default
data	ndarray	2-D array of shape (n_observations, n_variables).	required

Returns:

Type	Description
ndarray	Covariance matrix of shape (n_variables, n_variables).

cumsum

cumsum(values)

Cumulative sum of an array.

Parameters:

Name	Type	Description	Default
values	ndarray	Input array.	required

Returns:

Type	Description
ndarray	Cumulative sum with the same length as input.

ewma

ewma(values, span)

Exponentially weighted moving average.

Parameters:

Name	Type	Description	Default
values	ndarray	Input time series.	required
span	int	Decay span (alpha = 2 / (span + 1)).	required

Returns:

Type	Description
ndarray	EWMA-smoothed series of the same length.

Raises:

Type	Description
ValueError	If span < 1 or values is empty.

ewma_std

ewma_std(values, span)

Exponentially weighted moving standard deviation.

Parameters:

Name	Type	Description	Default
values	ndarray	Input time series.	required
span	int	Decay span (alpha = 2 / (span + 1)).	required

Returns:

Type	Description
ndarray	EWMA standard deviation series.

Raises:

Type	Description
ValueError	If span < 1 or values is empty.

kurtosis

kurtosis(values)

Excess kurtosis (fourth standardized moment minus 3).

Parameters:

Name	Type	Description	Default
values	ndarray	Input array (length >= 4).	required

Returns:

Type	Description
float	Excess kurtosis (0 for a normal distribution).

log_returns

log_returns(prices)

Logarithmic returns from a price series.

Computes log(p[i] / p[i-1]) for each consecutive pair.

Parameters:

Name	Type	Description	Default
prices	ndarray	Price series of length n.	required

Returns:

Type	Description
ndarray	Log returns of length n-1.

matrix_inverse

matrix_inverse(matrix)

Invert a square matrix using LU decomposition.

Parameters:

Name	Type	Description	Default
matrix	ndarray	Square matrix of shape (n, n).	required

Returns:

Type	Description
ndarray	Inverse matrix of shape (n, n).

Raises:

Type	Description
ValueError	If the matrix is singular or not square.

mean

mean(values)

Arithmetic mean of an array.

Parameters:

Name	Type	Description	Default
values	ndarray	Input array.	required

Returns:

Type	Description
float	Mean value.

Raises:

Type	Description
ValueError	If the array is empty.

power_iteration_eig

power_iteration_eig(matrix, num_components, max_iter=1000, tol=1e-10)

Eigendecomposition via power iteration.

Computes the top num_components eigenvalues and eigenvectors of a symmetric matrix using deflated power iteration.

Parameters:

Name	Type	Description	Default
matrix	ndarray	Symmetric square matrix.	required
num_components	int	Number of leading eigenvalues/vectors to compute.	required
max_iter	int	Maximum iterations per component.	1000
tol	float	Convergence tolerance.	1e-10

Returns:

Type	Description
tuple[ndarray, ndarray]	(eigenvalues, eigenvectors) where eigenvalues has shape (num_components,) and eigenvectors has shape (n, num_components) with columns as eigenvectors.

simple_returns

simple_returns(prices)

Simple (arithmetic) returns from a price series.

Computes (p[i] - p[i-1]) / p[i-1] for each consecutive pair.

Parameters:

Name	Type	Description	Default
prices	ndarray	Price series of length n.	required

Returns:

Type	Description
ndarray	Simple returns of length n-1.

skewness

skewness(values)

Sample skewness (third standardized moment).

Parameters:

Name	Type	Description	Default
values	ndarray	Input array (length >= 3).	required

Returns:

Type	Description
float	Skewness coefficient.

std_dev

std_dev(values, ddof=1)

Sample standard deviation with configurable degrees of freedom.

Parameters:

Name	Type	Description	Default
values	ndarray	Input array.	required
ddof	int	Delta degrees of freedom.	1

Returns:

Type	Description
float	Standard deviation.

variance

variance(values, ddof=1)

Sample variance with configurable degrees of freedom.

Parameters:

Name	Type	Description	Default
values	ndarray	Input array.	required
ddof	int	Delta degrees of freedom. Use 0 for population variance, 1 for sample variance (Bessel's correction).	1

Returns:

Type	Description
float	Variance of the input.

Raises:

Type	Description
ValueError	If the array has fewer elements than ddof + 1.

weighted_mean

weighted_mean(values, weights)

Weighted arithmetic mean.

Parameters:

Name	Type	Description	Default
values	ndarray	Input values.	required
weights	ndarray	Non-negative weights (same length as values). Need not sum to 1.	required

Returns:

Type	Description
float	Weighted mean.