Robustified Gaussian quasi-BIC for volatility

TL;DR

This paper introduces a robust model comparison method for non-ergodic volatility models with jumps, using density-power weighting and Gaussian quasi-likelihood normalization, ensuring consistency.

Contribution

It develops a new robust model selection framework for jump-contaminated volatility models, with proven consistency and practical numerical validation.

Findings

Proposed Schwarz-type statistics are model selection consistent.

Numerical experiments confirm theoretical properties.

Method effectively handles finite-activity jumps in volatility models.

Abstract

We develop a theoretical foundation for robust model comparison in a class of non-ergodic continuous volatility regression models contaminated by finite-activity jumps. Using the density-power weighting and the H\"{o}lder(-inequality)-based normalization of the conventional Gaussian quasi-likelihood function, we propose two Schwarz-type statistics and also establish their model selection consistency with respect to the minimal true parametric volatility coefficient. Numerical experiments are conducted to illustrate our theoretical findings.