# Forecasting with a Bivariate Hysteretic Time Series Model Incorporating Asymmetric Volatility and Dynamic Correlations

## TL;DR

This paper introduces a new financial model that captures dynamic volatility and correlations in financial assets using Bayesian methods and hysteresis.

## Contribution

The novelty lies in integrating asymmetric volatility and dynamic correlations within a multivariate hysteretic autoregressive model using Bayesian inference.

## Key findings

- The model effectively captures downside risk dynamics in financial time series.
- VaR forecasts from the model pass standard backtesting procedures.
- Results on real financial data show improved performance compared to the original model.

## 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.