Abstract: In this article, we propose a unified approach to estimating and modeling univariate time series. The approach applies to both linear and nonlinear time series models and can be used to discriminate non-nested nonlinear models. For example, it can discriminate between threshold autoregressive and bilinear models or between autoregressive and moving average models. It can also be used to estimate and discriminate between symmetric and asymmetric conditional heteroscedastic models commonly used in volatility studies of financial time series. The proposed approach is based on Gibbs sampling and may require substantial amounts of computing in some applications. We illustrate the proposed approach by some simulated and real examples. Comparison with other existing methods is also discussed.
Key words and phrases: Bayesian model selection, bilinear model, Gibbs sampler, mixed model, stochastic volatility, threshold autoregressive model.