bskernel

This package provides flexible auto-covariance kernel construction via inverse Fourier transforms of B-spline bases, as well as some handy tools for optimisation. Please note, if you have found yourself in the GitHub repo, please navigate here for the pkgdown page.

Installation

You can install the development version of bskernel from GitHub with

devtools::install_github("astfalckl/bskernel")

Quickstart

The bskernel package provides tools for constructing auto-covariance functions via the inverse Fourier transform of B-spline basis functions on the spectral domain. The workhorse functions are

• build_bspline_design_matrix
• reconstruct_acf

Below is a minimal example that recreates Figure 1 of the paper.

library(bskernel)

k <- 1 
knots <- seq(-0.125, 0.5, 0.125)
omega <- seq(0, 0.5, length.out = 100)
tau <- seq(0, 7.5, length = 100)

spline_bases <- build_bspline_design_matrix(omega, knots, k)

acfs <- sapply(1:4, function(i){
  idx <- rep(0, 4)
  idx[i] <- 1
  Re(reconstruct_acf(idx, knots, k, tau))
})

Note that reconstruct_acf() is designed to summate over a bases expansion, here we iteratively select the basis member. The spline and acf bases are plotted below (plotting code is suppressed, see .Rmd file).

Articles

I have written a number of tutorials:

• Maximum Likelihood with the Gaussian Likelihood
• Function reference

Citation

This package accompanies the paper

LC Astfalck. (2025). ‘’Universal modelling of auto-covariance functions via spline kernels’’. Submitted to the Journal of the Royal Statistical Society: Series B. [Available here.]