Forecast Comparison of Nonlinear Time Series Models of Us GDP : A Bayesian Approach

This thesis utilizes modern Bayesian tools to evaluate the forecasting performance of two of the most widely used nonlinear time series models of post-war US GDP, the Markov Switching (MS) model and the Self-Exciting threshold autoregressive (SETAR) model. We develop a clear, empirical ground for model selection, forecast comparison and forecast combination in the context of nonlinear economic time series. The use of the Bayesian methodology introduces an immediate framework to deal with nonlinearities. This holds not only in estimation, by treating nuisance parameters as unknown random variables, and in testing, by avoiding the approximation of unknown distributions of likelihood ratio statistics in order to find evidence of nonlinearity, but also in the choice of the best model according to its forecasting potential. To our knowledge, the literature avoids welcoming existing Bayesian methods in forecasting and comparison of nonlinear time series models; all known attempts from a Bayesian perspective are consumed only to the estimation part. Here we propose to use predictive likelihoods, an easy to adopt and to interpret criterion, as an alternative to classical forecast evaluation criterions like the root mean squared forecast error (RMSE). The advantage of our approach is very clear in the nonlinear time series framework that we examine. Preservation of computational resources, efficiency in manipulation of nuisance parameters, and parameter uncertainty are fully incorporated while we improve over individual forecasts by implementing Bayesian Model Averaging