An Open-model Forecast-error Taxonomy

We develop forecast-error taxonomies when there are unmodeled variables, forecast 'off-line'.  We establish three surprising results.  Even when an open system is correctly specified in-sample with zero intercepts, despite known future values of strongly exogenous variables, changes in dynamics can induce forecast failure when they have non-zero means.  The additional impact on forecast failure of incorrectly omitting such variables depends only on shifts in their means.  With no such shifts, there is no reduction in forecast failure from forecasting unmodeled variables relative to omitting them in 1-step or multi-step forecasts.  Simulation illustrations confirm these results.