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
- x
List
[ndarray
] ndependent element list of regressor
- eps
ndarray
Model residuals, ndependent by nobs
- sigma
ndarray
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
- kernel
str
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
- bandwidth
float
Bandwidth to use for the kernel. If not provided the optimal bandwidth will be estimated.
- x
See also
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 used in estimation
Parameter covariance
Optional configuration information used in covariance
Kernel used in estimation
Error covariance