Electricity consumption is often modelled as a function of temperature. Temperature is measured by daily heating degrees and cooling degrees. Heating degrees is 18
C minus the average daily temperature when the daily average is below 18 C; 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 dened as the average daily temperature minus 18 C when the daily average is above 18 C; 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.
An analyst fits the following model to a set of such data:
Where
a. What sort of ARIMA model is identied for ηt?
b. The estimated coecients are
Explain what the estimates of β1
and β2
tell us about electricity consumption.
c. Write the equation in a form more suitable for forecasting.
d. Describe how this model could be used to forecast electricity demand for the next 12 months.
e. Explain why the ηt
term should be modelled with an ARIMA model rather than modelling the data using a standard regression package. In your discussion, comment on the properties of the estimates, the validity of the standard regression results, and the importance of the ηt
model in producing forecasts.