Summary of the statistical analysis

The Fossil Fuel variable is world consumption of fossil fuels (i.e. coal, petroleum, and natural gas), measured in gigabarrels of oil equivalent per year. These data were pulled together from various sources, principally British Petroleum's Statistical Review of World Energy (2007) for oil and gas, and the History Database of the Environment, a publication of The Netherlands, for coal. Data from the 19th century are unreliable at best. Predictions for 2008 and later are based on my personal Hubbert analyses of coal, natural gas, conventional oil, and extra-heavy oil.

The Solar Activity variable is constructed from a trailing 11-year smooth of the annual sunspot numbers reported by the Royal Observatory of Belgium. The smoothing operation removes almost all of the cyclic activity, leaving only the average intensity of solar activity over the previous 11 years.

The dependent variable in this analysis is HadCrut3v, the global mean temperature "anomaly" as estimated by the Climate Prediction Unit of the University of East Anglia, 1850-2007, measured in degrees Celsius (1°C = 1.8°F). The term "anomaly" in this context means only that these are temperature differences from the 1961-90 global average, not absolute temperatures.

The statistical model used here is an AR(1) linear autoregressive model, which yields an R² of 87% and an F-statistic of 343 with 3 and 153 degrees of freedom. The model's coefficients and their statistics are summarized in the following table:

For the purposes of simulation, this model can be represented as a stochastic difference equation. Let X_t be temperature, Y_t be fossil fuel consumption, and Z_t be solar activity, all in year t. Then:

X_t+1 = (-0.201822) + (0.570075)X_t + (0.00114129)Y_t-25 + (0.00723698)Z_t + U_t ,

where {U} is a series of random i.i.d. variables with mean zero and standard deviation 0.09015.

Finally, here is a table of data for these variables: