The periodic zeta covariance function for Gaussian process regression

08/04/2022

∙

by   Giacomo Petrillo, et al.

∙

0

∙

share

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 ν which regulates the continuity and differentiability properties of the process in a way completely analogous to the parameter ν of the Matérn class of covariance functions. This makes the periodic zeta a good companion to add a power-law prior spectrum seasonal component to a Matérn prior for Gaussian process regression. It is also a close relative of the circular Matérn 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.