climatological use of daily averages as benchmarks, and it captures trend via a simple linear deterministic
function of time. We refer to this forecast as the “climatological forecast.”
The third benchmark forecast, unlike benchmarks one and two, is not at all naive; on the contrary,
it is a highly sophisticated forecast produced in real time by EarthSat. To produce their forecast, EarthSat
meteorologists pool their expert judgement with model-based numerical weather prediction (NWP)
forecasts from the National Weather Service, as well as forecasts from European, Canadian, and U.S. Navy
weather services. This blending of judgement with models is typical of best-practice modern weather
forecasting.
We were able to purchase approximately two years of forecasts from EarthSat. The sample period
runs from 10/11/99, the date when EarthSat began to archive their forecasts electronically and make them
publicly available, through 10/22/01. Each weekday, EarthSat makes a set of h-day ahead daily average
temperature forecasts, for h = 1, 2, ..., 11. EarthSat does not make forecasts on weekends.
We measure accuracy of all point forecasts using h-day-ahead root mean squared prediction error
(RMSPE). We assess point forecasting accuracy at horizons of h = 1, 2, ..., 11 days, because those are the
horizons at which EarthSat’s forecasts are available. We compute measures of the accuracy of our model
and the EarthSat model relative to that of the persistence and climatological benchmarks. RMPSE ratios
relative to benchmarks are called skill scores in the meteorological literature (Brier and Allen, 1951) and
U-statistics in the econometrics literature (Theil, 1966). Specifically, in an obvious notation, the skill score
relative to the persistence forecast is SWUe = (Γ,4-⅛, ~ Twh)2∣ У ,Twhe t ~ ^kɔ2, where Ts+ht = Tt is
the persistence forecast and Tt+h t is either the autoregressive forecast or the EarthSat forecast. The skill
score relative to the climatological forecast is SWlle = (7ζj.;,, - Twhe / У , - Twhe, where Tt+ht
denotes the climatological forecast, Tt+h t = β0 + β1 (t + h) + У^'ι5 ‰, and dh is a daily dummy.
A number of nuances merit discussion. First, for each of our time-series models, we estimate and
forecast recursively, using only the data that were available in real time. Thus our forecasts at any time
utilize no more average temperature information than do EarthSat’s. In fact, our forecasts are based on less
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