# arch.covariance.kernel.TukeyParzen¶

class arch.covariance.kernel.TukeyParzen(x, bandwidth=None, df_adjust=0, center=True, weights=None, force_int=False)[source]

Tukey-Parzen 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

$\begin{split}w=\begin{cases} 0.436 + 0.564 \cos{\pi z} & z\leq1 \\ 0 & z>1 \end{cases}\end{split}$

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.