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