RDP 2008-02: Combining Multivariate Density Forecasts Using Predictive Criteria Appendix A: Calculating the Predictive Likelihood

To calculate the predictive likelihood (reproduced below for convenience),

for each model k we use the multivariate normal distribution and take an average across multiple draws (j) from model k's predictive distribution of z_k,t+h. That is,

where n = 500 and is multivariate normal. The predictive distribution for each model was constructed via simulation as described in the main text. This is the same approach used by Andersson and Karlsson (2007).