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