fdars (version 0.3.3)

kernel.linear: Linear Covariance Function

Description

Computes the linear covariance function: $$k(s, t) = \sigma^2 (s - c)(t - c)$$

Usage

kernel.linear(variance = 1, offset = 0)

Value

A covariance function object of class 'kernel_linear'.

Arguments

variance

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

offset

Offset parameter \(c\) (default 0).

Details

The linear covariance function produces sample paths that are linear functions. It is useful when the underlying process is expected to have a linear trend.

See Also

kernel.polynomial, make.gaussian.process

Examples

# Generate linear function samples
cov_func <- kernel.linear(variance = 1)
t <- seq(0, 1, length.out = 50)
fd <- make.gaussian.process(n = 10, t = t, cov = cov_func)
plot(fd)