Modelling Football Data Using a GQL Algorithm based on Higher Ordered Covariances.

The modelling of the number of goals scored by a football team has been rarely studied in literature. This paper proposes a bivariate integer-valued autoregressive process of order 1 (BINAR(1)) that models the first and second half number of goals scored by a team in each league match. In this time series process, the innovations are considered to be bivariate Negative binomials since the goals scored express some variability than its means under both halves. However, a challenging issue is the estimation of the parameters of interest that include the vector of regression effects which influence the goals, the over-dispersion coefficients and the cross and serial dependence parameters. As at date, the generalized quasi-likelihood equation is the most suitable to estimate these parameters as it does not require the likelihood specification while it yields equally efficient estimates as likelihood-based approaches. The estimation of the over-dispersion requires the construction of high-ordered covariances which demands the working multivariate Gaussian normality. This assumption, as proved in previous studies, is more robust than the traditional Method of Moments. The BINAR(1) process is assessed on the Arsenal football data from the period 2005 to 2016.