Question

Consider the following time series data.

Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Value | 22 | 11 | 18 | 10 | 17 | 21 | 13 |

A) What type of pattern exists in the data?

The data appear to follow a seasonal pattern.

The data appear to follow a trend pattern.

The data appear to follow a horizontal pattern.

The data appear to follow a cyclical pattern.

B) Develop the three-month moving average forecasts for this time series.

Month | Time Series Value |
Forecast |
---|---|---|

1 | 22 | |

2 | 11 | |

3 | 18 | |

4 | 10 | ____ |

5 | 17 | ____ |

6 | 21 | ____ |

7 | 13 | ____ |

Compute MSE. (Round your answer to two decimal places.)

MSE = ____

What is the forecast for month 8? ____

C) Use *α* = 0.2 to compute the exponential smoothing
forecasts for the time series. (Round your answers to two decimal
places.)

Month | Time Series Value |
Forecast |
---|---|---|

1 | 22 | |

2 | 11 | ____ |

3 | 18 | ____ |

4 | 10 | ____ |

5 | 17 | ____ |

6 | 21 | ____ |

7 | 13 | ____ |

Compute MSE. (Round your answer to two decimal places.)

MSE = ____

What is the forecast for month 8? (Round your answer to two decimal places.) ____

D) Compare the three-month moving average approach with the
exponential smoothing approach using *α* = 0.2. Which
appears to provide more accurate forecasts based on MSE?

The three-month moving average provides a better forecast since
it has a larger MSE than the exponential smoothing using *α*
= 0.2.

The exponential smoothing using *α* = 0.2 provides a
better forecast since it has a smaller MSE than the three-month
moving average.

The exponential smoothing using *α* = 0.2 provides a
better forecast since it has a larger MSE than the three-month
moving average.

The three-month moving average provides a better forecast since
it has a smaller MSE than the exponential smoothing using
*α* = 0.2.

Answer #1

The data appear to follow a horizontal pattern.

b)

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

1 | 22 | |||

2 | 11 | |||

3 | 18 | |||

4 | 10 |
17.00 |
-7.00 | 49.00 |

5 | 17 |
13.00 |
4.00 | 16.00 |

6 | 21 |
15.00 |
6.00 | 36.00 |

7 | 13 |
16.00 |
-3.00 | 9.00 |

total | 110.00 | |||

average | 27.50 | |||

MSE= |
27.50 |
|||

Forecast= |
17.00 |

c)

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

1 | 22 | |||

2 | 11 |
22.00 |
-11.00 | 121.00 |

3 | 18 |
19.80 |
-1.80 | 3.24 |

4 | 10 |
19.44 |
-9.44 | 89.11 |

5 | 17 |
17.55 |
-0.55 | 0.30 |

6 | 21 |
17.44 |
3.56 | 12.66 |

7 | 13 |
18.15 |
-5.15 | 26.56 |

total | 252.88 | |||

average | 42.15 | |||

MSE= |
42.15 |
|||

Forecast= |
17.12 |

d)

The three-month moving average provides a better forecast since
it has a smaller MSE than the exponential smoothing using
*α* = 0.2.

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(i)
(ii)
(iii)
(iv)
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4
5
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Value
18
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