arch.covariance.kernel.CovarianceEstimate

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

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.