Forecasting volatility with asymmetric smooth transition dynamic range models

We propose a nonlinear smooth transition conditional autoregressive range (CARR) model for capturing smooth volatility asymmetries in international financial stock markets, building on recent work on smooth transition conditional duration modelling. An adaptive Markov chain Monte Carlo scheme is developed for Bayesian estimation, volatility forecasting and model comparison for the proposed model. The model can capture sign or size asymmetry and heteroskedasticity, such as that which is commonly observed in financial markets. A mixture proposal distribution is developed in order to improve the acceptance rate and the mixing issues which are common in random walk Metropolis‐Hastings methods. Further, the logistic transition function is employed and its main properties are considered and discussed in the context of the proposed model, which motivates a suitable, weakly informative prior which ensures a proper posterior distribution and identification of the estimators. The methods are illustrated using simulated data, and an empirical study also provides evidence in favour of the proposed model when forecasting the volatility in two financial stock markets. In addition, the deviance information criterion is employed to compare the proposed models with their limiting classes, the nonlinear threshold CARR models and the symmetric CARR model.