arch.covariance.kernel.Parzen¶

Parzen’s 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

\[\begin{split}w=\begin{cases}1-6z^{2}\left(1-z\right) & z\leq\frac{1}{2} \\ 2\left(1-z\right)^{3} & \frac{1}{2}<z\leq1 \\ 0 & z>1 \end{cases}\end{split}\]

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.