forecasts as relevant for weather derivatives. The results are mixed but ultimately encouraging, and they
point toward directions that may yield future forecasting improvements. We proceed as follows. In
Section 2 we discuss our data and our focus on modeling and forecasting daily average temperature, and we
report the results of time-series modeling. In section 3 we report the results of out-of-sample point and
density forecasting exercises. In section 4 we offer concluding remarks and highlight some pressing
directions for future research.
2. Time Series Weather Data and Modeling
We begin by discussing our choice of weather data and its collection. We are interested in daily
average temperature (T), which is widely reported and followed. Moreover, the heating degree days
(HDDs) and cooling degree days (CDDs) on which weather derivatives are commonly written are simple
transformations of daily average temperature. We directly model and forecast daily average temperature,
measured in degrees Fahrenheit, for each of four measurement stations (Atlanta, Chicago, Las Vegas,
Philadelphia) for 1/1/60 through 11/05/01, resulting in 15,285 observations per measurement station. Each
of the cities is one of the ten for which temperature-related weather derivatives are traded at the CME. In
earlier and longer versions of this article, Campbell and Diebold (2002, 2003), we report results for all ten
cities, which are qualitatively identical. We obtained the data from Earth Satellite (EarthSat) corporation;
they are precisely those used to settle temperature-related weather derivative products traded on the CME.
The primary underlying data source is the National Climactic Data Center (NCDC), a division of the
National Oceanographic and Atmospheric Administration. Each of the measurement stations supplies its
data to the NCDC, and those data are in turn collected by EarthSat.
Before proceeding to detailed modeling and forecasting results, it is useful to get an overall feel for
the daily average temperature data. In Figure 1 we plot the daily average temperature series for the last five
years of the sample. The time-series plots reveal strong and unsurprising seasonality in average
temperature: in each city, the daily average temperature moves repeatedly and regularly through periods of
high temperature (summer) and low temperature (winter). Importantly, however, the seasonal fluctuations
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