Estimating Gaussian Mixture Autoregressive model with Sequential Monte Carlo algorithm: A parallel GPU implementation

In this paper, we propose using Bayesian sequential Monte Carlo (SMC) algorithm to estimate the univariate Gaussian mixture autoregressive (GMAR) model. The prominent benefit of the Bayesian approach is that the stationarity restriction required by the GAMR model can be straightforwardly imposed via prior distribution. In addition, compared to MCMC (Markov Chain Monte Carlo) and other simulation based algorithms, the SMC is robust to multimodal posteriors, and capable of providing fast on-line estimation when new data is available. Furthermore, it has a linear computational complexity and is ready for parallelism. To demostrate the SMC, an empirical application with US GDP growth data is considered. After estimation, we conduct the Bayesian model selection to evaluate the empirical evidence for different GMAR models. To facilitate the realization of this compute-intensive estimation, we parallelize the SMC algorithm on a nVidia CUDA compatible Graphical Process Unit (GPU) card.