  We develop a new statistical model to analyse time-varying ranking data. The
model can be used with a large number of ranked items, accommodates exogenous
time-varying covariates and partial rankings, and is estimated via maximum
likelihood in a straightforward manner. Rankings are modelled using the
Plackett-Luce distribution with time-varying worth parameters that follow a
mean-reverting time series process. To capture the dependence of the worth
parameters on past rankings, we utilize the conditional score in the fashion of
the generalized autoregressive score (GAS) models. Simulation experiments show
that small-sample properties of the maximum-likelihood estimator improve
rapidly with the length of the time series and suggest that statistical
inference relying on conventional Hessian-based standard errors is usable even
for medium-sized samples. As an illustration, we apply the model to the results
of the Ice Hockey World Championships. We also discuss applications to rankings
based on underlying indices, repeated surveys, and non-parametric efficiency
analysis.
