  Deciding which predictors to use plays an integral role in deriving
statistical models in a wide range of applications. Motivated by the challenges
of predicting events across a telecommunications network, we propose a
semi-automated, joint model-fitting and predictor selection procedure for
linear regression models. Our approach can model and account for serial
correlation in the regression residuals, produces sparse and interpretable
models and can be used to jointly select models for a group of related
responses. This is achieved through fitting linear models under constraints on
the number of non-zero coefficients using a generalisation of a recently
developed Mixed Integer Quadratic Optimisation approach. The resultant models
from our approach achieve better predictive performance on the motivating
telecommunications data than methods currently used by industry.
