Weather Forecasting for Weather Derivatives

average temperature information: our forecast for day t+1 made on day t is based on daily average
temperature through 11:59 PM of day t, whereas the EarthSat forecast for day t+1, which is not released
until 6:45 AM on day t+1, potentially makes use of the history of temperature through 6:45 AM of day
t+1. Second, we make forecasts using our models only on the dates that EarthSat made forecasts. In
particular, we make no forecasts on weekends. Hence, our accuracy comparisons proceed by averaging
squared errors over precisely the same days as those corresponding to the EarthSat errors. This ensures a
fair apples-to-apples comparison.

We report RMSPEs in Table 1 at horizons of h = 1, 3, 5, 7, 9, and 11 days, for all cities and
forecasting models. In addition, we graph skill scores as a function of horizon, against the persistence
forecast in Figure 7 and against the climatological forecast in Figure 8, for all cities and horizons. The
results are the same for all cities, so it is not necessary to discuss them individually by city. The results
most definitely do differ, however, across models and horizons, as we now discuss. We first discuss the
performance of the time-series forecasts, and then we discuss the EarthSat forecasts.

Let us consider first the forecasting performance of the persistence, climatological, and
autoregressive models across the various horizons. First consider the comparative performance of the
persistence and climatological forecasts. When h=1, the climatological forecasts are much worse than the
persistence forecasts, reflecting the fact that persistence in daily average temperature renders the
persistence forecast quite accurate at very short horizons. As the horizon lengthens, however, this result is
reversed: the persistence forecast becomes comparatively poor, as the temperature today has rather little to
do with the temperature, for example, nine days from now.

Second, consider the performance of the autoregressive forecasts relative to the persistence and
climatological forecasts. Even when h=1, the autoregressive forecasts consistently outperform the
persistence forecast, and their relative superiority increases with horizon. The autoregressive forecasts also
outperform the climatological forecasts at short horizons, but their comparative superiority decreases with
horizon. The performance of the autoregressive forecast is commensurate with that of the climatological

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