Robust Bayesian estimation in conditionally heteroscedastic time series models

TL;DR

This paper introduces a robust Bayesian estimation method for heteroscedastic time series models using density power divergence, improving reliability under outliers and contamination in financial data.

Contribution

It extends the DPD framework to Bayesian inference in heteroscedastic models, establishing asymptotic properties and demonstrating robustness through simulations and real data.

Findings

The DPD-based posterior converges to a normal distribution centered at the MDPDE.

The proposed estimator maintains robustness under data contamination.

Empirical results show improved performance on financial time series.

Abstract

Outliers can seriously distort statistical inference by inducing excessive sensitivity in the likelihood function, thereby compromising the reliability of Bayesian estimation. To address this issue, we develop a robust Bayesian estimation method for conditionally heteroscedastic time series models by extending the density power divergence (DPD) framework to the Bayesian setting. The resulting DPD-based posterior distribution, controlled by a tuning parameter, achieves a smooth balance between efficiency and robustness. We establish the asymptotic properties of the proposed estimator; specifically, the DPD-based posterior is shown to satisfy a Bernstein-von Mises type theorem, converging to a normal distribution centered at the minimum DPD estimator (MDPDE). Furthermore, the corresponding Bayes estimator, defined as the posterior mean under the DPD-based posterior (EDPE), is asymptotically equivalent to the MDPDE. Monte Carlo simulations based on GARCH(1,1) models confirm that the proposed EDPE performs well under both uncontaminated and contaminated data, maintaining robustness where the ordinary Bayes estimator becomes severely biased. An empirical application to BTC-USD returns further demonstrates the practical advantages of the proposed robust Bayesian framework for financial time series analysis.