Weather Forecasting for Weather Derivatives

longer than those commonly emphasized by meteorologists. Hence the supply-side questions, as with the
demand-side questions, are intimately related to weather modeling and forecasting.

Curiously, however, it seems that little thought has been given to the crucial question of how best
to approach the weather modeling and forecasting that underlies weather derivative demand and supply.
The meteorological weather forecasting literature focuses primarily on short-horizon point forecasts
produced from structural physical models of atmospheric conditions (see, for example, the overview in
Tribia, 1997). Although such an approach is best for helping one decide how warmly to dress tomorrow, it
is not at all obvious that it is best for producing the long-horizon density forecasts relevant for weather
derivatives. In particular, successful forecasting does not necessarily require a structural model, and in the
last thirty years statisticians and econometricians have made great strides in using nonstructural models of
time-series trend, seasonal, cyclical components to produce good forecasts, including long-horizon density
forecasts. (For a broad overview see Diebold, 2004.)

In this paper, then, motivated by considerations related to the weather derivatives market, we take a
nonstructural time-series approach to weather modeling and forecasting, systematically asking whether it
proves useful. We are not the first to adopt a time-series approach, although the literature is sparse and
inadequate for our purposes. The analyses of Harvey (1989), Hyndman and Grunwald (2000), Milionis and
Davies (1994), Visser and Molenaar (1995), Jones (1996), and Pozo et al. (1998) suggest its value, for
example, but they do not address the intra-year temperature forecasting relevant to our concerns. Seater
(1993) studies long-run temperature trend, but little else. Cao and Wei (2001) and Torro, Meneu and Valor
(2001) - each of which was written independently of the present paper - consider time-series models of
average temperature, but their models are more restrictive and their analyses more limited.

We progress by providing insight into both conditional mean dynamics and conditional variance
dynamics of daily average temperature as relevant for weather derivatives; strong conditional variance
dynamics are a central part of the story. We also highlight the differences between the distributions of
weather and weather innovations. Finally, we evaluate the performance of time series point and density

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