Constructing narrowest pathwise bootstrap prediction bands using threshold accepting

Typically, prediction bands for path-forecasts are constructed pointwise, while inference relates to the whole forecasted path. In general, no closed form analytical solution is available for pathwise bands in finite samples. We consider a direct construction approach based on bootstrapped prediction bands. The resulting highly complex optimization problem is tackled using the local search heuristic of threshold accepting. A comparison with pointwise and asymptotic bands is provided, demonstrating superior properties of the proposed bands in small samples. Finally, a real application shows the practical implications of using an appropriate tool for generating the prediction bands.