arch.covariance.kernel.CovarianceEstimate

class arch.covariance.kernel.CovarianceEstimate(short_run, one_sided_strict, columns=None, long_run=None, one_sided=None)

Covariance estimate using a long-run covariance estimator

Parameters

• short_run (ndarray) -- The short-run covariance estimate.

• one_sided_strict (ndarray, default None) -- The one-sided strict covariance estimate.

• columns ({None, list[str]}) -- Column labels to use if covariance estimates are returned as DataFrames.

• long_run (ndarray, default None) -- The long-run covariance estimate. If not provided, computed from short_run and one_sided_strict.

• one_sided_strict -- The one-sided-strict covariance estimate. If not provided, computed from short_run and one_sided_strict.

Notes

If \(\Gamma_0\) is the short-run covariance and \(\Lambda_1\) is the one-sided strict covariance, then the long-run covariance is defined

\[\Omega = \Gamma_0 + \Lambda_1 + \Lambda_1^\prime\]

and the one-sided covariance is

\[\Lambda_0 = \Gamma_0 + \Lambda_1.\]

Methods

Properties

long_run	The long-run covariance estimate.
one_sided	The one-sided covariance estimate.
one_sided_strict	The one-sided strict covariance estimate.
short_run	The short-run covariance estimate.