Electricity consumption is often modelled as a function of temperature. Temperature is measured by daily heating degrees and cooling degrees. Heating degrees is 18C minus the average daily temperature when the daily average is below 18C; 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 defined as the average daily temperature minus 18C when the daily average is above 18C; otherwise it is zero. Let denote the monthly total of kilowatt-hours of electricity used, let 1, denote the monthly total of heating degrees, and let 2,t denote the monthly total of cooling degrees. An analyst fits the following model to a set of such data: y=x,t+x2.t+n where 1 = B and y= logy), x=/1,t and 2,t=2,t. a. [3 marks] What sort of ARIMA model has the analyst identified for nt? (For example, is it an ARIMA(1,0,0)(0,0,1)12 model?) 3 b. [2 marks] The estimated coefficients are Parameter Estimate s.e. Z P-value 31 0.0077 0.0015 4.98 0.000 2 0.0208 0.0023 9.23 0.000 1 0.5830 0.0720 8.10 0.000 12 0.5373 0.0856 6.27 0.000 24 0.4667 0.0862 -5.41 0.000 Explain what the estimates of , and tell us about electricity consumption. c. [5 marks] Write the equation in a form more suitable for forecasting. (Handwritten answers are fine, but they must be embedded in the PDF file that is submitted.) d. [3 marks] Describe how this model could be used to forecast electricity demand for the next 12 months. e. [2 marks} Explain why the nt term should be modelled with an ARIMA model rather than modelling the data using a standard ordinary least squares regression approach. In your discussion, comment on the properties of the estimates, the validity of the standard regression results, and the importance of the nt model in producing forecasts.