Bayesian Nonparametric Density Autoregression with Lag Selection

We develop a Bayesian nonparametric autoregressive model applied to flexibly estimate general transition densities exhibiting nonlinear lag dependence. Our approach is related density regression using Dirichlet process mixtures, with the Markovian likelihood defined through conditional distribution obtained from mixture. This results in extension of mixtures-of-experts formulation. address computational challenges posterior sampling that arise structure likelihood. The base illustrated synthetic data classical for population dynamics, as well series waiting times between eruptions Old Faithful Geyser. study inferences available before extending methodology include automatic relevance detection among pre-specified set lags. Inference global and local selection explored additional simulation studies, methods are analysis an annual time pink salmon abundance stream Alaska. further explore compare estimation performance alternative configurations proposed model. Supplementary materials online.