fChange (version 0.2.1)

LongRun: Long Run Covariance Operator Estimation for Functional Time Series

Description

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

Usage

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

Arguments

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

Value

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

References

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

See Also

opt_bandwidth

Examples

# NOT RUN {
# 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

# }