Here Σ t is the n t × n t correlation matrix at level t and matrix F t = [y t-1 (D t ), 1 n t ]; the detailed expression for Q t can be found in the literature. Uniform prior distributions were assumed for correlation hyperparameters φ 1 , φ 2 , and an empirical Bayes approach employed. For posterior inference, these parameters were set equal to their posterior mode.