The periodic zeta covariance function for Gaussian process regression
Abstract
I consider the Lerch-Hurwitz or periodic zeta function as covariance function of a periodic continuous-time stationary stochastic process. The function can be parametrized with a continuous index which regulates the continuity and differentiability properties of the process in a way completely analogous to the parameter of the Mat\'ern class of covariance functions. This makes the periodic zeta a good companion to add a power-law prior spectrum seasonal component to a Mat\'ern prior for Gaussian process regression. It is also a close relative of the circular Mat\'ern covariance, and likewise can be used on spheres up to dimension three. Since this special function is not generally available in standard libraries, I explain in detail the numerical implementation.
Cite
@article{arxiv.2208.02596,
title = {The periodic zeta covariance function for Gaussian process regression},
author = {Giacomo Petrillo},
journal= {arXiv preprint arXiv:2208.02596},
year = {2022}
}