arch.covariance.kernel.QuadraticSpectral¶

class arch.covariance.kernel.QuadraticSpectral(x: ndarray | DataFrame | Series, bandwidth: float | None = None, df_adjust: int = 0, center: bool = True, weights: ndarray | DataFrame | Series | None = None, force_int: bool = False)[source]¶

Quadratic-Spectral (Andrews’) kernel covariance estimation.

Parameters:¶

x: ndarray | DataFrame | Series¶

The data to use in covariance estimation.

bandwidth: float | None = None¶

The kernel’s bandwidth. If None, optimal bandwidth is estimated.

df_adjust: int = 0¶

Degrees of freedom to remove when adjusting the covariance. Uses the number of observations in x minus df_adjust when dividing inner-products.

center: bool = True¶

A flag indicating whether x should be demeaned before estimating the covariance.

weights: ndarray | DataFrame | Series | None = None¶

An array of weights used to combine when estimating optimal bandwidth. If not provided, a vector of 1s is used. Must have nvar elements.

force_int: bool = False¶

Force bandwidth to be an integer.

Notes

The kernel weights are computed using

\[\begin{split}w=\begin{cases} 1 & z=0\\ \frac{3}{x^{2}}\left(\frac{\sin x}{x}-\cos x\right),x=\frac{6\pi z}{5} & z>0 \end{cases}\end{split}\]

where \(z=\frac{h}{H}, h=0, 1, \ldots, H\) where H is the bandwidth.

Methods

Properties

bandwidth	The bandwidth used by the covariance estimator.
bandwidth_scale	The power used in optimal bandwidth calculation.
centered	Flag indicating whether the data are centered (demeaned).
cov	The estimated covariances.
force_int	Flag indicating whether the bandwidth is restricted to be an integer.
kernel_const	The constant used in optimal bandwidth calculation.
kernel_weights	Weights used in covariance calculation.
name	The covariance estimator's name.
opt_bandwidth	Estimate optimal bandwidth.
rate	The optimal rate used in bandwidth selection.