Reconsider Prob. 20.5-3. Ralph Billett realizes that the last-value method is considered to be the naive forecasting method, so he wonders whether he should be using another method. Therefore, he has decided to use the available Excel templates that consider seasonal effects to apply various statistical forecasting methods retrospectively to the past three years of data and compare their MAD values.

(a) Determine the seasonal factors for the four quarters.

(b) Apply the last-value method.

(c) Apply the averaging method.

(d) Apply the moving-average method based on the four most recent quarters of data.

(e) Apply the exponential smoothing method with an initial estimate of 25 and a smoothing constant of α = 0.25.

(f) Apply exponential smoothing with trend with smoothing constants of α = 0.25 and ß = 0.25. Use initial estimates of 25 for the expected value and 0 for the trend.

(g) Compare the MAD values for these methods. Use the one with the smallest MAD to forecast sales in Quarter 1 of next year.

(h) Use the forecast in part (g) and the seasonal factors to make long-range forecasts now of the sales in the remaining quarters of next year

Prob. 20.5-3

Ralph Billett is the manager of a real estate agency. He now wishes to develop a forecast of the number of houses that will be sold by the agency over the next year. The agency's quarter-by-quarter sales figures over the last three years are shown below.

(a) Determine the seasonal factors for the four quarters.

(b) After considering seasonal effects, use the last-value method to forecast sales in Quarter 1 of next year.

(c) Assuming that each of the quarterly forecasts is correct, what would the last-value method forecast as the sales in each of the four quarters next year?

(d) Based on his assessment of the current state of the housing market, Ralph's best judgment is that the agency will sell 100 houses next year. Given this forecast for the year, what is the quarter-by-quarter forecast according to the seasonal factors?