The Centerville Water Department provides water for the entire town and outlying areas. The number of acre-feet of water consumed in each of the four seasons of the three preceding years is shown below.
(a) Determine the seasonal factors for the four seasons.
(b) After considering seasonal effects, use the last-value method to forecast water consumption next winter.
(c) Assuming that each of the forecasts for the next three seasons is correct, what would the last-value method forecast as the water consumption in each of the four seasons next year?
(d) After considering seasonal effects, use the averaging method to forecast water consumption next winter.
(e) After considering seasonal effects, use the moving-average method based on four seasons to forecast water consumption next winter.
(f) After considering seasonal effects, use the exponential smoothing method with an initial estimate of 46 and a smoothing constant of α = 0.1 to forecast water consumption next winter.
(g) Compare the MAD values of these four forecasting methods when they are applied retrospectively to the last three years.
(h) Calculate and compare the MSE values of these four forecasting methods when they are applied retrospectively to the last three years.