Linear Covariance Function

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

Usage

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

Arguments

variance

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

offset

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

Value

A covariance function object of class 'kernel_linear'.

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)