A doubly self-exciting Poisson model for describing scoring levels in NBA basketball

Abstract

In this article, Poisson time series models are considered to describe the number of field goals made by a basketball team or player at both the game (within-season) and the minute (within-game) level. The model is endowed with a doubly self-exciting structure, following the INGARCH(1,1) specification. To estimate the model at the within-game level, a divide-and-conquer procedure is carried out under a Bayesian framework. Then, we perform a clustering of the players in terms of their similarity according to the corresponding posterior distributions of key model parameters. The model is tested with National Basketball Association (NBA) teams and players from the 2018–2019 season.