Title: Bayesian analysis of predictive non-Homogeneous hidden Markov models using Polya-Gamma data augmentation
Authors: Ioannis Vrontos - Athens University of Economics and Business (Greece)
Loukia Meligkotsidou - University of Athens (Greece)
Constandina Koki - Athens University of Economics and Business (Greece) [presenting]
Abstract: Non-Homogeneous hidden Markov Models (NHMMs) are considered for forecasting univariate time series. We introduce two state NHMMs where the time series are modeled via different predictive regression models for each state. Furthermore, the time-varying transition probabilities depend on exogenous variables through a logistic function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. To address this problem, we use a new latent variable scheme, that utilizes the Polya-Gamma class of distributions. Given an available set of predictors, we allow for model uncertainty regarding the predictors that affect the series both linearly -- in the mean -- and non-linearly -- in the transition matrix. Variable selection and inference on the model parameters are based on a MCMC scheme with reversible jump steps. Single-step and multiple-steps-ahead predictions are obtained based on the most probable model, median probability model or a Bayesian Model Averaging (BMA) approach. Simulation experiments, including an empirical study on real financial data, illustrate the performance of our algorithm in various setups, in terms of mixing properties, model selection and predictive ability.