A simple forecasting method for weekly sales of flash drives used by a local com

Question

A simple forecasting method for weekly sales of flash drives used by a local
computer dealer is to form the average of the two most recent sales figures.
Suppose sales for the drives for the past 12 weeks were
Week: 1 2 3 4 5 6 7 8 9 10 11 12
Sales: 86 75 72 83 132 65 110 90 67 92 98 73
a. Determine the one-step-ahead forecasts made for periods 3 through 12 using
this method.
b. Determine the forecast errors for these periods.
c. Compute the MAD, the MSE, and the MAPE based on the forecast errors
computed in part (b).

Explanation / Answer

1.00 The one-step-ahead forecasts made for periods 3 through 12 Week Sales Forecasts Simple avg. 1 86 2 75 3 72 80.5 4 83 73.5 5 132 77.5 6 65 107.5 7 110 98.5 8 90 87.5 9 67 100 10 92 78.5 11 98 79.5 12 73 95 2.00 Forecast error can be a calendar forecast error or a cross-sectional forecast error, when we want to summarize the forecast error over a group of units. If we observe the average forecast error for a time-series of forecasts for the same product or phenomenon, then we call this a calendar forecast error or time-series forecast error. Reference class forecasting has been developed to reduce forecast error. Combining forecasts has also been shown to reduce forecast error The forecast error needs to be calculated using actual data as a base. Forecast Errors = | A – F | Forecast Error as Percentage = | A – F | / A Where: A = Actual demand F = Forecast demand Week Sales Forecasts Simple avg. Forecast Errors Forecast Errors % 1 86 2 75 3 72 80.5 -8.5 -11.81 4 83 73.5 9.5 11.45 5 132 77.5 54.5 41.29 6 65 107.5 -42.5 -65.38 7 110 98.5 11.5 10.45 8 90 87.5 2.5 2.78 9 67 100 -33 -49.25 10 92 78.5 13.5 14.67 11 98 79.5 18.5 18.88 12 73 95 -22 -30.14 3.00 Compute the MAD, the MSE, and the MAPE based on the forecast errors MAD: A common way of tracking the extent of forecast error is to add the absolute period errors for a series of periods and divide by the number of periods MAD = |A – F| / n Where: |A – F| = Total of absolute forecast errors for the periods n = Number of periods Week Sales Forecasts Simple avg. Forecast Errors Absolute deviation 1 86 2 75 3 72 80.5 -8.5 8.5 4 83 73.5 9.5 9.5 5 132 77.5 54.5 54.4 6 65 107.5 -42.5 42.5 7 110 98.5 11.5 11.5 8 90 87.5 2.5 2.5 9 67 100 -33 33 10 92 78.5 13.5 13.5 11 98 79.5 18.5 18.5 12 73 95 -22 22 215.9 NO of periods 10 MAD 21.59 Standard deviation ( Approx)= 26.9875 MSE = (Error for each period)²/ Number of forecast periods Week Sales Forecasts Simple avg. Forecast Errors Absolute deviation Squared Errors 1 86 2 75 3 72 80.5 -8.5 8.5 72.25 4 83 73.5 9.5 9.5 90.25 5 132 77.5 54.5 54.4 2959.36 6 65 107.5 -42.5 42.5 1806.25 7 110 98.5 11.5 11.5 132.25 8 90 87.5 2.5 2.5 6.25 9 67 100 -33 33 1089 10 92 78.5 13.5 13.5 182.25 11 98 79.5 18.5 18.5 342.25 12 73 95 -22 22 484 215.9 7164.11 NO of periods 10 10 MAD 21.59 MSE 716.411 MAPE = ( |A – F| / A ) % / n Week Sales Forecasts Simple avg. Forecast Errors Absolute deviation MAPE 1 86 2 75 3 72 80.5 -8.5 8.5 11.81 4 83 73.5 9.5 9.5 11.45 5 132 77.5 54.5 54.4 41.21 6 65 107.5 -42.5 42.5 65.38 7 110 98.5 11.5 11.5 10.45 8 90 87.5 2.5 2.5 2.78 9 67 100 -33 33 49.25 10 92 78.5 13.5 13.5 14.67 11 98 79.5 18.5 18.5 18.88 12 73 95 -22 22 30.14 256.02 Mape %= 25.60

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