linearmodels.system.covariance.KernelCovariance

class KernelCovariance(x, eps, sigma, full_sigma, *, gls=False, debiased=False, constraints=None, kernel='bartlett', bandwidth=None)[source]

Kernel (HAC) covariance estimation for system regression

Parameters:
xlist[ndarray]

ndependent element list of regressor

epsndarray

Model residuals, ndependent by nobs

sigmandarray

Covariance matrix estimator of eps

glsbool

Flag indicating to compute the GLS covariance estimator. If False, assume OLS was used

debiasedbool

Flag indicating to apply a small sample adjustment

kernelstr

Name of kernel to use. Supported kernels include:

  • “bartlett”, “newey-west” : Bartlett’s kernel

  • “parzen”, “gallant” : Parzen’s kernel

  • “qs”, “quadratic-spectral”, “andrews” : Quadratic spectral kernel

bandwidthfloat

Bandwidth to use for the kernel. If not provided the optimal bandwidth will be estimated.

Notes

If GLS is used, the covariance is estimated by

\[(X'\Omega^{-1}X)^{-1}\tilde{S}(X'\Omega^{-1}X)^{-1}\]

where X is a block diagonal matrix of exogenous variables and where \(\tilde{S}\) is a estimator of the covariance of the model scores based on the model residuals and the weighted X matrix \(\Omega^{-1/2}X\).

When GLS is not used, the covariance is estimated by

\[(X'X)^{-1}\hat{S}(X'X)^{-1}\]

where \(\hat{S}\) is a estimator of the covariance of the model scores.

Attributes:
bandwidth

Bandwidth used in estimation

cov

Parameter covariance

cov_config

Optional configuration information used in covariance

kernel

Kernel used in estimation

sigma

Error covariance

Methods

Properties

bandwidth

Bandwidth used in estimation

cov

Parameter covariance

cov_config

Optional configuration information used in covariance

kernel

Kernel used in estimation

sigma

Error covariance