A note on predictive densities based on composite likelihood methods

Whenever the computation of data distribution is unfeasible or inconvenient, the classical predictive procedures prove not to be useful. These rely, after all, on the conditional distribution of the future random variable, which is also unavailable. This paper considers a notion of composite likelihood for specifying composite predictive distributions, viewed as surrogates for true unknown predictive distribution. In particular, the focus is on the pairwise likelihood obtained as a weighted product of likelihood factors related to bivariate events associated with both the sample data and future observation. The specification of the weights, andmore generally the evaluation of the frequentist properties of alternative pairwise predictive distributions, is performed by considering the mean square prediction error of the associated predictors and the expected Kullback–Liebler loss of the related predictive densities. Finally, simple examples concerning autoregressive models are presented.