Bayesian Forecasting for a Logistic Mixture Double Autoregressive Model

To capture the dynamic relationship between financial time series and covariates, we consider a logistic mixture double autoregressive model with explanatory variables. The model is composed of two double autoregressive models whose mixing ratio is time‐varying and is driven by a logistic regression structure. By introducing a series of Bernoulli distributed latent variables, a complete data likelihood is obtained, which makes the Bayesian inference feasible. Based on this likelihood, a new Markov chain Monte Carlo algorithm is developed to address the parameter estimation problem. The heteroscedasticity test problem for the underlying process is also addressed by means of Bayes factor. The performances of the proposed methods are evaluated via simulations. Finally, the proposed model is applied to the Shanghai Stock Exchange Index data set.