Quantile forecasting based on a bivariate hysteretic autoregressive model with GARCH errors and time ‐varying correlations

To understand and predict chronological dependence in the second‐order moments of asset returns, this paper considers a multivariate hysteretic autoregressive (HAR) model with generalized autoregressive conditional heteroskedasticity (GARCH) specification and time‐varying correlations, by providing a new method to describe a nonlinear dynamic structure of the target time series. The hysteresis variable governs the nonlinear dynamics of the proposed model in which the regime switch can be delayed if the hysteresis variable lies in a hysteresis zone. The proposed setup combines three useful model components for modeling economic and financial data: (1) the multivariate HAR model, (2) the multivariate hysteretic volatility models, and (3) a dynamic conditional correlation structure. This research further incorporates an adapted multivariate Student t innovation based on a scale mixture normal presentation in the HAR model to tolerate for dependence and different shaped innovation components. This study carries out bivariate volatilities, Value at Risk, and marginal expected shortfall based on a Bayesian sampling scheme through adaptive Markov chain Monte Carlo (MCMC) methods, thus allowing to statistically estimate all unknown model parameters and forecasts simultaneously. Lastly, the proposed methods herein employ both simulated and real examples that help to jointly measure for industry downside tail risk.