Year: 2022
Type: preprint
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 $ν$ 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.
Source: arXiv (Cornell University)
Author: Petrillo, Giacomo
Institution: University of Florence
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4290057974