Question

Month | 1 2 3 4 5 6 7 |

Value | 24 15 21 13 19 21 16 |

a) Develop a three-month moving average for this time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation. MSE:_______ The forecast for month 8________

b) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation. MSE_____ The forecast for month 8 _____

c) Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE. If required, round your answer to two decimal places. α =______

Answer #1

a)

month | value | forecast | |error| | error^2 |

1 | 24 | |||

2 | 15 | |||

3 | 21 | |||

4 | 13 | 20.00 |
-7.00 | 49.00 |

5 | 19 | 16.33 |
2.67 | 7.11 |

6 | 21 | 17.67 |
3.33 | 11.11 |

7 | 16 | 17.67 |
-1.67 | 2.78 |

total | 70.00 | |||

average | 17.50 | |||

MSE= |
17.50 |
|||

Forecast= |
18.67 |

b)

month | value | forecast | error | error^2 |

1 | 24 | |||

2 | 15 | 24.00 |
-9.00 | 81.00 |

3 | 21 | 22.20 |
-1.20 | 1.44 |

4 | 13 | 21.96 |
-8.96 | 80.28 |

5 | 19 | 20.17 |
-1.17 | 1.36 |

6 | 21 | 19.93 |
1.07 | 1.14 |

7 | 16 | 20.15 |
-4.15 | 17.20 |

total | 182.42 | |||

average | 30.40 | |||

MSE= |
30.40 |
|||

Forecast= |
19.32 |

c()

from trial and error : α =0.41

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