Empirical simultaneous prediction regions for path-forecasts

This paper investigates the problem of constructing prediction regions for forecast trajectories 1 to H periods into the future - a path forecast. We take the more general view that the null model is only approximative and in some cases it may be altogether unavailable. As a consequence, one cannot derive the usual analytic expressions nor resample from the null model as is usually done when bootstrap methods are used. The paper derives methods to construct approximate rectangular regions for simultaneous probability coverage which correct for serial correlation. The techniques appear to work well in simulations and in an application to the Greenbook path-forecasts of growth and inflation.