On a Bivariate Hysteretic AR-GARCH Model with Conditional Asymmetry in Correlations

This paper investigates a conditionally dynamic asymmetric structure in correlations when multivariate time series follow a hysteretic autoregressive GARCH process that exhibits nonlinear switching in mean, volatility, and correlation. The hysteresis variable in the proposed model controls regime switching and time-varying delay. This new model allows for distinct responses to negative return shocks, as it can flexibly explore the possibility of asymmetry in the conditional correlation of two target variables. We employ an adaptive Bayesian MCMC method for the parameter estimation and quantile forecasting, which includes value-at-risk and volatility. We conduct backtesting to measure the effectiveness of value-at-risk forecasting, illustrate the proposed methods by using both simulated and real examples, and jointly measure for industry downside tail risk. Lastly, we evaluate the accuracy of the volatility forecast and determine whether there is persistence of conditional asymmetry in conditional correlation in the target time series.