science. In his well-known text, for example, Wilks (1995, p. 159) notes that “[Statistical weather
forecasting] methods are still viable and useful at very short lead times (hours in advance) or very long lead
times (weeks or more in advance) for which NWP information is either not available with sufficient
promptness or accuracy, respectively.” Indeed, in many respects our results are simply an extensive
confirmation of Wilks’ assertion in the context of weather derivatives, which are of great current interest.
Ultimately, our present view on weather forecasting for weather derivatives is that climatological
forecasts are what we need, but that standard point climatological forecasts - effectively little more than
daily averages - are much too restrictive. Instead, we seek “generalized climatological forecasts” from
richer models tracking entire conditional distributions, and modern time-series statistical methods may have
much to contribute. We view the present paper as a “call to action,” with our simple model representing a
step toward a fully generalized climatological forecast, but with many important issues remaining
unexplored. Here we briefly discuss a few that we find particularly intriguing.
One of the contributions of this paper is our precise quantification of daily average temperature
conditional variance dynamics. But richer dynamics might be beneficially permitted in both lower-ordered
conditional moments (the conditional mean) and higher-ordered conditional moments (such as the
conditional skewness and kurtosis). As regards the conditional mean, one could introduce explanatory
variables, as in Visser and Molenaar (1995), who condition on a volcanic activity index, sunspot numbers,
and a southern oscillation index. Relevant work also includes Jones (1996) and Pozo et al. (1998), but
those papers use annual data and therefore miss the seasonal patterns in both conditional mean and
conditional variance dynamics so crucial for weather derivatives demand and supply. One could also allow
for nonlinear effects, most notably stochastic regime switching, which might aid, for example, in the
detection of El Nino and La Nina events. (See Richman and Montroy, 1996, and also Zwiers and von
Storch, 1990.) As regards the conditional skewness and kurtosis, one could model them directly, as for
example with the autoregressive conditional skewness model of Harvey and Siddique (1999).
Alternatively, one could directly model the evolution of the entire conditional density, as in Hansen (1994).
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