Question

John has collected the following information on the amount of tips he has collected from parking cars the last seven nights.

Day Tips

1 18

2 22

3 17

4 18

5 28

6 20

7 12

a. Compute the 3-day moving averages for the time series. (5 points)

b. Compute the mean square error for the forecasts. (4 points)

c. Compute the mean absolute deviation for the forecasts. (4 points)

d. Forecast John's tips for day 8. (4 points)

Answer #1

a) Three period moving average = forecast for fourth period
y_{4} = (y_{3}+y_{2}+y_{1})/3

day | Tips | three period moving average |

1 | 18 | NA |

2 | 22 | NA |

3 | 17 | NA |

4 | 18 | 19 |

5 | 28 | 19 |

6 | 20 | 21 |

7 | 12 | 22 |

day 8 | 20 |

b)

day | Tips | three period moving average | error |

1 | 18 | ||

2 | 22 | ||

3 | 17 | ||

4 | 18 | 19 | -1 |

5 | 28 | 19 | 9 |

6 | 20 | 21 | -1 |

7 | 12 | 22 | -10 |

20 |

MSE = ((-1)^{2} +
(-1)^{2}+(9)^{2}+(-10)^{2})/4 = 45.75

c) mean absolute deviation for the forecasts = (1+9+1+10)/4 = 5.25

d) Forecast for day 8 = (28 + 20 +12)/3 = 20

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