Weather Forecasting for Weather Derivatives

example to El Nino, La Nina, changes in the jet stream, or various other global factors.

Now consider assessing independence. In the last four columns of Figure 9, we show the
correlograms of the first four powers of z, taken to a maximum displacement of ten years, together with
asymptotic 95% Bartlett bands under the iid null hypothesis. The results are mixed, but a common pattern
of some positive serial correlation is often apparent.

All told, we view our CumHDD distributional forecasting performance as encouraging, although
there is clear room for improvement. Evidently the effects of small specification errors in the daily model,
which have negligible consequences for near-term forecasting, cumulate as the horizon lengthens,
producing large consequences for longer-term forecasting. The error in forecasting CumHDD is of course
the sum of the many component daily errors, and the variance of that sum is the sum of the variances plus
the sum of all possible pairwise covariances. Hence tiny and hard-to-detect but slowly-decaying serial
correlation in 1-day-ahead daily average temperature forecasting errors may cumulate over long horizons.
In future work beyond the scope of this paper, it will be of interest to attempt to address the specification
error issue by modeling and forecasting CumHDD directly. Presently, in contrast, we fit only a single
(daily) average temperature model, which we estimate by minimizing a loss function corresponding to 1-
day-ahead mean squared prediction error, and we then use the model to produce forecasts at many different
horizons, all of which feed into our CumHDD forecasts.

4. Concluding Remarks and Directions for Future Research

Weather modeling and forecasting are crucial to both the demand and supply sides of the weather
derivatives market. On the demand side, to assess the potential for hedging against weather surprises and
to formulate the appropriate hedging strategies, one needs to determine how much “weather noise” exists
for weather derivatives to eliminate, and that requires weather modeling and forecasting. On the supply
side, standard approaches to arbitrage-free pricing are irrelevant in weather derivative contexts, and so the
only way to price options reliably is again by modeling and forecasting the underlying weather variable.
Rather curiously, it seems that little thought has been given to the crucial question of how best to approach

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