Abstract
This study explores asymmetric volatility structures within multivariate hysteretic autoregressive (MHAR) models that incorporate conditional correlations, aiming to flexibly capture the dynamic behavior of global financial assets. The proposed framework integrates regime switching and time-varying delays governed by a hysteresis variable, enabling the model to account for both asymmetric volatility and evolving correlation patterns over time. We adopt a fully Bayesian inference approach using adaptive Markov chain Monte Carlo (MCMC) techniques, allowing for the joint estimation of model parameters, Value-at-Risk (VaR), and Marginal Expected Shortfall (MES). The accuracy of VaR forecasts is assessed through two standard backtesting procedures. Our empirical analysis involves both simulated data and real-world financial datasets to evaluate the model's effectiveness in capturing downside risk dynamics. We demonstrate the application of the proposed method on three pairs of daily log returns involving the S&P500, Bank of America (BAC), Intercontinental Exchange (ICE), and Goldman Sachs (GS), present the results obtained, and compare them against the original model framework.