8.3 Electricity consumption is often modeled as a function of temperature. Temperature is measured by daily heating de-

grees and cooling degrees. Heating degrees is 65±F minus the average daily temperature when the daily average is below 65±F; otherwise it is zero. This provides a measure of our need to heat ourselves as temperature falls. Cooling degrees measures our need to cool ourselves as the temperature rises.

It is de¯ned as the average daily temperature minus 65±F when the daily average is above 65±F; otherwise it is zero. Let Yt denote the monthly total of kilowatt-hours of electricity used, let X1;t denote the monthly total of heating degrees, and let X2;t denote the monthly total of cooling degrees.

Pankratz (1991) ¯ts the following model to a set of such data:

Y 0 t = b0 + b1X0 1;t + b2X0 2;t + Nt where (1 ¡ B)(1 ¡ B12)Nt =

1 ¡ µ1B 1 ¡ Á12B12 ¡ Á24B24 et and Y 0 t = log(Yt), X01

;t =

p X1;t and X0 2;t =

p X2;t.