fdars (version 0.3.3)

kernel.periodic: Periodic Covariance Function

Description

Computes the periodic covariance function: $$k(s, t) = \sigma^2 \exp\left(-\frac{2\sin^2(\pi|s-t|/p)}{\ell^2}\right)$$

Usage

kernel.periodic(variance = 1, length_scale = 1, period = 1)

Value

A covariance function object of class 'kernel_periodic'.

Arguments

variance

Variance parameter \(\sigma^2\) (default 1).

length_scale

Length scale parameter \(\ell\) (default 1).

period

Period parameter \(p\) (default 1).

Details

The periodic covariance function produces sample paths that are periodic with the specified period. It is useful for modeling seasonal or cyclical patterns in functional data.

See Also

kernel.gaussian, make.gaussian.process

Examples

# Generate periodic function samples
cov_func <- kernel.periodic(period = 0.5, length_scale = 0.5)
t <- seq(0, 2, length.out = 100)
fd <- make.gaussian.process(n = 5, t = t, cov = cov_func)
plot(fd)