Modelling Time-Varying Rankings with Autoregressive and Score-Driven Dynamics

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