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

Abstract

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.