Weather Forecasting for Weather Derivatives

Notes to Tables and Figures

Table 1: We show each forecast’s root mean squared error, measured in degrees Fahrenheit.

Figure 1: Each panel displays a time-series plot of daily average temperature, 1996-2001.

Figure 2: Each panel displays a kernel density estimate of the unconditional distribution of daily average
temperature, 1960-2001. In each case, we employ the Epanechnikov kernel and select the bandwidth using
Silverman’s rule, h=O.9σN~⁰².

Figure 3: Each panel displays the residuals from an unobserved-components model,
η = Trend_t + Sea9ona0_t + ∑‰ P,Λ-,∙ ^{+ σ}∕^εr 1996-2001.

Figure 4: Each panel displays a kernel density estimate of the distribution of the residuals from our daily
average temperature model, T_t - Trend_t - Seasonal_t -       p_i∙T^,_f._i∙. In each case, we employ the

Epanechnikov kernel and select the bandwidth using Silverman’s rule, h=O.9σN~⁰².

Figure 5: Each panel displays sample autocorrelations of the squared residuals from our daily average
temperature model, ,T_t - Tregd_t - Setasothtel_t - jɪ p,.7ζ,,.j², together with Bartlett’s approximate ninety-
five percent confidence intervals under the null hypothesis of white noise.

Figure 6: Each panel displays a time series of estimated conditional standard deviations (σ_f) of daily
average temperature, where o_t = ɪ^i ^γ_c             + γ_s^sin^2π<7-∣∣θj + Ctejl₁ + βo^₁, 1996-2001.

Figure 7: Each panel displays the ratio of a forecast’s RMSPE to that of a persistence forecast, for 1-day-
ahead through 11-day-ahead horizons. The solid line refers to the EarthSat forecast, and the dashed line
refers to the autoregressive forecast. The forecast evaluation period is 10/11/99 - 10/22/01.

Figure 8: Each panel displays the ratio of a forecast’s RMSPE to that of a climatological forecast, for 1-
day-ahead through 11-day-ahead horizons. The solid line refers to the EarthSat forecast, and the dashed
line refers to the autoregressive forecast. The forecast evaluation period is 10/11/99 - 10/22/01.

Figure 9: Each row displays a histogram for z and correlograms for four powers of z, the probability
integral transform of cumulative November-March HDDs, 1960-2000. Dashed lines indicate approximate
ninety-five percent confidence intervals in the iid U(0,1) case of correct conditional calibration.

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