arch.bootstrap.IIDBootstrap.cov

IIDBootstrap.cov(func: Callable[[...], ndarray | DataFrame | Series], reps: int = 1000, recenter: bool = True, extra_kwargs: dict[str, Any] | None = None) → float | ndarray[tuple[int, ...], dtype[float64]][source]

Compute parameter covariance using bootstrap.

Parameters:
func: Callable[[...], ndarray | DataFrame | Series]

Callable function that returns the statistic of interest as a 1-d array.

reps: int = 1000

Number of bootstrap replications. Must be at least 1.

recenter: bool = True

Whether to center the bootstrap variance estimator on the average of the bootstrap samples (True) or to center on the original sample estimate (False).

extra_kwargs: dict[str, Any] | None = None

Dictionary of extra keyword arguments to pass to func.

Returns:

Bootstrap covariance estimator. If func returns complex values, this is the complex Hermitian covariance, which uses the conjugate transpose, and a complex128 array.

Return type:

numpy.ndarray

Raises:

  • TypeError – If func is not callable, reps is not an int, recenter is not a bool, or extra_kwargs is not a dict.

  • ValueError – If reps is less than 1, or extra_kwargs has a key that is the name of bootstrapped data.

Notes

func must have the signature

func(*args, **kwargs)

where *args and **kwargs are the bootstrap version of the data used in the bootstrap, and any extra_kwargs are appended to **kwargs. The function returns a scalar, a 0-dimensional array or a 1-dimensional array-like. A params argument is not passed, so only the nonparametric bootstrap can be used.

Examples

Bootstrap covariance of the mean

>>> from arch.bootstrap import IIDBootstrap
>>> import numpy as np
>>> def func(x):
...     return x.mean(axis=0)
>>> y = np.random.randn(1000, 3)
>>> bs = IIDBootstrap(y)
>>> cov = bs.cov(func, 1000)

Bootstrap covariance using a function that takes additional input

>>> def func(x, stat='mean'):
...     if stat=='mean':
...         return x.mean(axis=0)
...     elif stat=='var':
...         return x.var(axis=0)
>>> cov = bs.cov(func, 1000, extra_kwargs={'stat':'var'})

Note

Note this is a generic example and so the class used should be the name of the required bootstrap.