Estimate Long-run Covariance Kernel

Estimate the long-run covariance kernel for functional data. That is, solve \( C_{\epsilon}(t,t') = \sum_{l=-\inf}^{\inf} \text{Cov}(\epsilon_0(t), \epsilon_l(t')) \) with sequence \((\epsilon_i : i \in \mathbb{Z})\) defined as the centered data (can center based on changes if given).

Usage

long_run_covariance(
  X,
  h = 2 * ncol(X)^(1/5),
  K = bartlett_kernel,
  changes = NULL
)

Arguments

X

A dfts object or data which can be automatically converted to that format. See dfts().

h

The window parameter parameter for the estimation of the long run covariance kernel. The default value is h=2*ncol(X)^(1/5). Note there exists an internal check such that \(h=min(h,ncol(X)-1)\) when alternative options are given.

K

Function indicating the kernel to use if \(h>0\).

changes

Vector of numeric change point locations. Can be NULL.

Value

Symmetric data.frame of numerics with dim of ncol(data) x ncol(data).

Examples

result <- long_run_covariance(electricity,2)