arch.covariance.kernel.TukeyHanning

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

Tukey-Hanning 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

\[\begin{split}w=\begin{cases} \frac{1}{2} + \frac{1}{2} \cos{\pi z} & z\leq1 \\ 0 & z>1 \end{cases}\end{split}\]

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.