Time Series Mean Level and Stochastic Volatility Modeling by Smooth Transition Autoregressions: A BAYESIAN Approach

In this paper, we propose a Bayesian approach to model the level and the variance of (financial) time series by the special class of nonlinear time series models known as the logistic smooth transition autoregressive models, or simply the LSTAR models. We first propose a Markov Chain Monte Carlo (MCMC) algorithm for the levels of the time series and then adapt it to model the stochastic volatilities. The LSTAR order is selected by three information criteria: the well-known AIC and BIC, and by the deviance information criteria, or DIC. We apply our algorithm to a synthetic data and two real time series, namely the canadian lynx data and the SP500 returns.