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

arXiv: https://arxiv.org/abs/2101.04040 · HTML: https://mlsanity.com/paper/2101.04040/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2021.

## Built on by (most cited first, 2 of 2)

- [Time Series Analysis of Rankings: A GARCH-Type Approach](https://mlsanity.com/paper/2502.05102/) (2025)
- [Score-Driven Rating System for Sports](https://mlsanity.com/paper/2604.09143/) (2026)

## Abstract (arXiv)

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 the 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 utilise the conditional score in the fashion of the generalised autoregressive score (GAS) models. Simulation experiments show that the 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. In an empirical study, 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.