fChange (version 0.2.1)

fun_heavy_tailed: Simulate Heavy Tailed Independent Functional Data

Description

It generates a heavy tail independent functional observations of sample size n

Usage

fun_heavy_tailed(n, nbasis, df = 3, basis = NULL, rangeval = c(0, 1),
  ...)

Arguments

n

Sample size of generated functional data. A strictly positive integer

nbasis

Number of basis functions used to represent functional observations

df

Degrees of freedom of the T-distribution to construct the functional observations. The default value is 3

basis

A functional basis object defining the basis. It can be the class of basisfd, fd, fdPar. As a default it is set to be a Fourier basis

rangeval

A vector of length 2 containing the initial and final values of the interval over which the functional data object can be evaluated. As a default it is set to be [0,1].

...

Further arguments to pass

Value

An independent functional data sample (class fd) containing:

coefs

The coefficient array

basis

A basis object

fdnames

A list containing names for the arguments, function values and variables

Details

The implementation of this function is very similar to fun_IID. The heavy tail functional observations are generated based on a linear combination of basis functions where the \(i\)-th linear combination coefficient has a t-distribution with df - degrees of freedom.

References

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

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)

See Also

Data2fd, fun_IID, fun_AR, fun_MA

Examples

# NOT RUN {
fdata1 = fun_heavy_tailed(n=100, nbasis=25)
fdata2 = fun_heavy_tailed(n=100, nbasis=25, df=4)

# }