A comparison of unconstrained parameterisations for additive mean and covariance matrix modelling

Covariance models for multivariate normal data must ensure the positive definiteness of the covariance matrix. Computational scalability for handling large samples is further desirable. We propose flexible covariance modelling by reparameterising the covariance matrix according to two different approaches, namely the matrix logarithm and the modified Cholesky decomposition. The performances of the proposed additive covariance models (ACM) are compared on an electricity load modelling application.