On the precision matrix of an irregularly sampled AR(1) process

TL;DR

This paper derives an analytical expression for the precision matrix of irregularly sampled AR(1) processes and provides efficient algorithms for density evaluation and simulation, implemented in an R package.

Contribution

It introduces a novel analytical formula for the precision matrix of irregular AR(1) processes and offers efficient computational algorithms.

Findings

Analytical expression for the precision matrix

Efficient algorithms for density evaluation

Implementation in R package irregulAR1

Abstract

Irregularly sampled AR(1) processes appear in many computationally demanding applications. This text provides an analytical expression for the precision matrix of such a process, and gives efficient algorithms for density evaluation and simulation, implemented in the R package irregulAR1.