LongRun: Long Run Covariance Operator Estimation for Functional Time...
In fChange: Change Point Analysis in Functional Data

Description Usage Arguments Value References See Also Examples

This function estimates the long run covariance operator of a given functional data sample and its estimated eigenelements.

1	LongRun(fdobj, h, kern_type = "BT", is_change = TRUE, ...)

`fdobj`	A functional data object
`h`	The bandwidth parameter. It is strictly non-zero. Choosing the bandwidth parameter to be zero is identical to estimating covariance operator assuming iid data.
`kern_type`	Kernel function to be used for the estimation of the long run covariance function. The choices are `c("BT", "PR", "SP", "FT")` which are respectively, bartlett, parzen, simple and flat-top kernels. By default the function uses a `"barlett"` kernel.
`is_change`	If `TRUE` then the data is centered considering the change in the mean function.
`...`	Further arguments to pass

`e_fun`	Eigenfunctions of the estimated long run covariance function
`e_val`	Eigenvalues of the estimated long run covariance function
`covm`	Coefficient matrix of the estimated long run covariance operator.
`contour_plot`	The estimated covariance function C(t,s) surface plot if `plot=TRUE`

Aue A., Rice G., Sonmez O. (2017+), Detecting and dating structural breaks in functional data without dimension reduction (https://arxiv.org/pdf/1511.04020.pdf)

Rice G. and Shang H. L. (2017), A plug-in bandwidth selection procedure for long run covariance estimation with stationary functional time series, Journal of Time Series Analysis, 38(4), 591-609

opt_bandwidth

# Generate FAR(1) process
fdata = fun_AR(n=100, nbasis=31, order=1, kappa=0.9)
# Estimate the Long run covrariance
C_hat = LongRun(fdata, h=2)
C_hat$e_fun # eigenfunctions of Long Run Cov
C_hat$e_val # eigenvalues of Long Run Cov
C_hat$covm # Estimated covariance matrix