# Question

A manufacturer sells a certain product in batches of 100 to wholesalers. The following table shows the quarterly sales figure for this product over the last several years.

The company incorporates seasonal effects into its forecasting of future sales. It then uses exponential smoothing (with seasonality) with a smoothing constant of α = 0.1 to make these forecasts. When starting the forecasting, it uses the average sales over the past four quarters to make the initial estimate of the seasonally adjusted constant level A for the underlying constant-level model.

(a) Suppose that the forecasting started at the beginning of 2011. Use the data for 2010 to determine the seasonal factors and then determine the forecast of sales for each quarter of 2011.

(b) Suppose that the forecasting started at the beginning of 2012. Use the data for both 2010 and 2011 to determine the seasonal factors and then determine the forecast of sales for each quarter of 2012.

(c) Suppose that the forecasting started at the beginning of 2014. Use the data for 2010 through 2013 to determine the seasonal factors and then determine the forecast of sales for each quarter of 2014.

(d) Under the assumptions of the constant-level model, the forecast obtained for any period of one year also provides the best available forecast at that time for the same period in any subsequent year. Use the results from parts (a), (b), and (c) to record the forecast of sales for Quarter 4 of 2014 when entering Quarter 4 of 2011, 2012, and 2014, respectively.

(e) Evaluate whether it is important to incorporate seasonal effects into the forecasting procedure for this particular product.

(f) Evaluate how well the constant-level assumption of the constant-level model (after incorporating seasonal effects) appears to hold for this particular product.

The company incorporates seasonal effects into its forecasting of future sales. It then uses exponential smoothing (with seasonality) with a smoothing constant of α = 0.1 to make these forecasts. When starting the forecasting, it uses the average sales over the past four quarters to make the initial estimate of the seasonally adjusted constant level A for the underlying constant-level model.

(a) Suppose that the forecasting started at the beginning of 2011. Use the data for 2010 to determine the seasonal factors and then determine the forecast of sales for each quarter of 2011.

(b) Suppose that the forecasting started at the beginning of 2012. Use the data for both 2010 and 2011 to determine the seasonal factors and then determine the forecast of sales for each quarter of 2012.

(c) Suppose that the forecasting started at the beginning of 2014. Use the data for 2010 through 2013 to determine the seasonal factors and then determine the forecast of sales for each quarter of 2014.

(d) Under the assumptions of the constant-level model, the forecast obtained for any period of one year also provides the best available forecast at that time for the same period in any subsequent year. Use the results from parts (a), (b), and (c) to record the forecast of sales for Quarter 4 of 2014 when entering Quarter 4 of 2011, 2012, and 2014, respectively.

(e) Evaluate whether it is important to incorporate seasonal effects into the forecasting procedure for this particular product.

(f) Evaluate how well the constant-level assumption of the constant-level model (after incorporating seasonal effects) appears to hold for this particular product.

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