Nonparametric Bayesian Method And Its Application In Time Series

Nonparametric method and Bayesian theory are two important branches of modern statis-tics. During the last decade they both have a good number of positive results in time series analysis, while nonparametric Bayesian method has few applications. In this paper, we intro-duce a latent variable into autoregressive time series model in a Baysian framework, assuming this latent variable comes from a Dirichlet process. And we apply nonparametric method to let the data "decide" the posterior distribution of the latent variable. We apply the model to both the simulation data and the empirical data. It suggests our model works well when there is heterogeneity such as periodicity and bimodal. Our method also needs only a few assumptions, and thus is more robust than parametric autoregressive model.