What is the MAD for the three-period moving-average forecast as of period 15?

What is the MAPE for the three-period moving average forecast as of period 15?

What is the MAD for the four-period moving average forecast as of period 15?

What is the MAPE for the four-period moving average forecast as of period 15?

Which forecast is the best (the three-period or four-period simple moving-average forecast method)?

FlyingDisc, Inc. has recorded the number of disc golf bags it has sold in each of the last 15 months of business. Use the recorded demand data below to develop three-period and four-period simple moving-average forecasts for disc golf bags. Round off all calculations to two decimal places. Maintaining two decimal places is required for all calculations. Period Demand Period 890 920 895 865 910 880 850 865 890 890 12 13 14 15 925 10

## Expert Answer

Following table illustrate and presents relevant data leading to determination of Moving average Forecast , MAD and MAPE

Period | Demand | Forecast value – 3 period moving average | Absolute deviation ( AD) | Absolute Percentage Error ( APE) | Forecast value – 4 period moving average | Absolute deviation (AD) | Absolute Percentage Error ( APE) |

1 | 850 | ||||||

2 | 890 | ||||||

3 | 925 | ||||||

4 | 880 | 888.33 | 8.33 | 0.94 | |||

5 | 860 | 898.33 | 38.33 | 4.27 | 886.25 | 26.25 | 2.96 |

6 | 890 | 888.33 | 1.67 | 0.19 | 888.75 | 1.25 | 0.14 |

7 | 920 | 876.67 | 43.33 | 4.94 | 888.75 | 31.25 | 3.52 |

8 | 895 | 890.00 | 5.00 | 0.56 | 887.5 | 7.5 | 0.85 |

9 | 865 | 901.67 | 36.67 | 4.07 | 891.25 | 26.25 | 2.95 |

10 | 910 | 893.33 | 16.67 | 1.87 | 892.5 | 17.5 | 1.96 |

11 | 880 | 890.00 | 10.00 | 1.12 | 897.5 | 17.5 | 1.95 |

12 | 850 | 885.00 | 35.00 | 3.95 | 887.5 | 37.5 | 4.23 |

13 | 865 | 880.00 | 15.00 | 1.70 | 876.25 | 11.25 | 1.28 |

14 | 890 | 865.00 | 25.00 | 2.89 | 876.25 | 13.75 | 1.57 |

15 | 900 | 868.33 | 31.67 | 3.65 | 871.25 | 28.75 | 3.30 |

Sum = | 266.67 | 30.15 | 218.75 | 24.70 |

Following are to be noted :

a) Three Period moving average Forecast :

Ft = ( Dt-1 + Dt-2 + Dt-3) / 3

b) Four period moving average forecast :

Ft =( Dt-1 + Dt-2 + Dt-3 + Dt-4)/4

Ft = Forecast for period t

Dt-1 = Demand for period t-1

Dt-2 = Demand for period t-2

Dt-3 = Demand for period t-3

Dt-4 = demand for period t-4

c) Thus forecast for period 16 using 4 period moving average = ( 850 + 865 + 890 + 900 ) /4 = 876.25

d) MAD for three period moving average = Sum of absolute deviations (AD) / 12 = 266.67/12 = 22.22

e) MAPE for three period moving average = Sum of absolute percentage error / 12 = 30.15/12 = 2.51

f) MAD for four period moving average = Sum of absolute deviations (AD) /11 = 218.75 / 11 = 19.88

g) MAPE for four period moving average = Sum of absolute percentage error /11 = 24.70/11 = 2.24

Since both MAD as well as MAPE for four period moving average is less than MAD and MAPE of three period moving average , Four Period moving average is a better forecast