forecast roughly by the time h=4, indicating that the cyclical dynamics captured by the autoregressive
model via the inclusion of lagged dependent variables, which are responsible for its superior performance
at shorter horizons, are not very persistent and therefore not readily exploited for superior forecast
performance at longer horizons.
Now let us compare the forecasting performance of the autoregressive model and the EarthSat
model. When h=1, the EarthSat forecasts are much better than the autoregressive forecasts (which in turn
are better then either the persistence or climatological forecasts). Figures 7 and 8 make clear, however, that
the EarthSat forecasts outperform the autoregressive forecasts by progressively less as the horizon
lengthens, with nearly identical performance obtaining by the time h=8. One could even make a case that
the point forecasting performances of EarthSat and our three-component model become indistinguishable
before h=8 (say, by h=5) if one were to account for the sampling error in the estimated RMSPEs and for the
fact that the EarthSat information set for any day t actually contains a few hours of the next day.
All told, we view our model’s point forecasting performance as neither particularly encouraging
nor particularly discouraging, at the longer horizons of relevance for weather derivatives (one to six
months, say). Its point forecasting performance is not particularly encouraging: although it appears no
worse than its competitors, it also appears no better. But its point forecasting performance is also not
particularly discouraging: the nature of temperature dynamics simply makes temperature very difficult to
forecast at long horizons, whether by our method or any other, as all point forecasts revert fairly quickly to
the climatological forecast, and hence all long-horizon forecasts are “equally poor.”
It is crucial to recognize, however, that a key object in any statistical analysis involving weather
derivatives, and indeed the key object for the central issue weather derivative pricing, is the entire
conditional density of the future weather outcome. The point forecast is the conditional mean, which
describes just one feature of that conditional density, namely its location. Hence the fact that the long-
horizon conditional mean estimate produced by our model is no better that produced by the climatological
model does not imply that our model or framework fails to deliver value-added. On the contrary, a great
-12-