arch.covariance.kernel.ParzenGeometric

class arch.covariance.kernel.ParzenGeometric(x, bandwidth=None, df_adjust=0, center=True, weights=None, force_int=False)

Parzen's Geometric kernel covariance estimation.

Parameters

• x (array_like) -- The data to use in covariance estimation.

• bandwidth (float, default None) -- The kernel's bandwidth. If None, optimal bandwidth is estimated.

• df_adjust (int, default 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, default True) -- A flag indicating whether x should be demeaned before estimating the covariance.

• weights (array_like, default 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, default False) -- Force bandwidth to be an integer.

Notes

The kernel weights are computed using

\[\begin{split}w=\begin{cases} \frac{1}{1+z} & z\leq1 \\ 0 & z>1 \end{cases}\end{split}\]

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.