Path forecasts, defined as sequences of individual forecasts, generated by vector autoregressions are widely used in applied work. It has been recognized that a profound econometric analysis often requires, besides the path forecast, a joint prediction region that contains the whole future path...

Path forecasts, defined as sequences of individual forecasts, generated by vector autoregressions are widely used in applied work. It has been recognized that a profound econometric analysis requires, besides the path forecast, a joint prediction region that contains the whole future path with a...

The predictive likelihood is of particular relevance in a Bayesian setting when the purpose is to rank models in a forecast comparison exercise. This paper discusses how the predictive likelihood can be estimated for any subset of the observable variables in linear Gaussian state-space models...