Weather Forecasting for Weather Derivatives

squared standardized residuals; there is no significant deviation from white noise behavior, indicating that
the fitted model (1) is adequate.

3. Time-Series Weather Forecasting

Armed with a hopefully adequate time-series model for daily average temperature, we now proceed
to examine its performance in out-of-sample weather forecasting. We begin by examining its performance
in short-horizon point forecasting, despite the fact that short horizons and point forecasts are not of
maximal relevance for weather derivatives, in order to compare our performance to that of a very
sophisticated leading meteorological forecast. One naturally suspects that the much larger information set
on which the meteorological forecast is based will result in superior short-horizon point forecasting
performance, but even if so, of great interest is the question of how quickly and with what pattern the
superiority of the meteorological forecast deteriorates with forecast horizon.

We then progress to assess the performance of our model’s long-horizon density forecasts, which
are of maximal interest in weather derivative contexts, given the underlying option pricing considerations.
Simultaneously, we also move to forecasting HDD_t rather than T_t. This lets us match the most common
weather derivative “underlying,” and it also lets us explore the effects of using a daily model to produce
much longer-horizon density forecasts.

Point Forecasting

We assess the short-term accuracy of daily average temperature forecasts based on our
seasonal+trend+cycle model. In what follows, we refer to those forecasts as “autoregressive forecasts,” for
obvious reasons. We evaluate the autoregressive forecasts relative to three benchmark competitors, which
range from rather naive to very sophisticated. The first benchmark forecast is a no-change forecast. The
no-change forecast, often called the “persistence forecast” in the climatological literature, is the minimum
mean squared error forecast at all horizons if daily average temperature follows a random walk.

The second benchmark forecast is from a more sophisticated two-component (seasonal+trend)
model. It captures (daily) seasonal effects via day-of-year dummy variables, in keeping with the common

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