Predictive information criterion for jump diffusion processes

TL;DR

This paper introduces a new information criterion for selecting models of ergodic jump diffusion processes using high-frequency data, incorporating novel estimates of transition densities.

Contribution

It develops an Akaike-type information criterion tailored for jump diffusion processes and provides new estimates of their transition densities.

Findings

The criterion effectively distinguishes between models with high accuracy.

New estimates improve the understanding of jump diffusion transition densities.

The method demonstrates reliable model selection in high-frequency sampling scenarios.

Abstract

In this paper, we address a model selection problem for ergodic jump diffusion processes based on high-frequency samples. We evaluate the expected genuine log-likelihood function and derive an Akaike-type information criterion based on the threshold-based quasi-likelihood function. In the derivation process, we also give new estimates of the transition density of jump diffusion processes. We also provide the relative selection probability of the proposed information criterion.