  Ranking lists are often provided at regular time intervals by one or multiple
rankers in a range of applications, including sports, marketing, and politics.
Most popular methods for rank-order data postulate a linear specification for
the latent scores, which determine the observed ranks, and ignore the temporal
dependence of the ranking lists. To address these issues, novel nonparametric
static (ROBART) and autoregressive (ARROBART) models are introduced, with
latent scores defined as nonlinear Bayesian additive regression tree functions
of covariates. To make inferences in the dynamic ARROBART model, closed-form
filtering, predictive, and smoothing distributions for the latent time-varying
scores are derived. These results are applied in a Gibbs sampler with data
augmentation for posterior inference. The proposed methods are shown to
outperform existing competitors in simulation studies, and the advantages of
the dynamic model are demonstrated by forecasts of weekly pollster rankings of
NCAA football teams.
