A State Space Approach to Evaluate Multi-horizon Forecasts

We propose a state space modeling framework to evaluate a set of forecasts that target
the same variable but are updated along the forecast horizon. The approach
decomposes forecast errors into three distinct horizon-specific processes, namely, bias,
rational error and implicit error, and attributes forecast revisions to corrections for these
forecast errors. We derive the conditions under which forecasts that contain error that is
irrelevant to the target can still present the second moment bounds of rational forecasts.
By evaluating multi-horizon daily maximum temperature forecasts for Melbourne,
Australia, we demonstrate how this modeling framework analyzes the dynamics of the
forecast revision structure across horizons. Understanding forecast revisions is critical
for weather forecast users to determine the optimal timing for their planning decision.