Question

Consider the following time series data.

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

Value | 24 | 13 | 20 | 12 | 19 | 23 | 15 |

(a)

Construct a time series plot.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Month. The vertical axis ranges from 0 to 30 and is labeled: Time Series Value. The points are plotted from left to right at regular increments of 1 month starting at month 1. The points appear to vary randomly between 12 to 24 on the vertical axis. The plot reaches its maximum time series value at month 7.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Month. The vertical axis ranges from 0 to 30 and is labeled: Time Series Value. The points are plotted from left to right at regular increments of 1 month starting at month 1. The points appear to vary randomly between 12 to 24 on the vertical axis. The plot reaches its maximum time series value at month 1.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Month. The vertical axis ranges from 0 to 30 and is labeled: Time Series Value. The points are plotted from left to right at regular increments of 1 month starting at month 1. The points appear to vary randomly between 7 to 19 on the vertical axis. The plot reaches its maximum time series value at month 1.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Month. The vertical axis ranges from 0 to 30 and is labeled: Time Series Value. The points are plotted from left to right at regular increments of 1 month starting at month 1. The points appear to vary randomly between 7 to 19 on the vertical axis. The plot reaches its maximum time series value at month 7.

What type of pattern exists in the data?

The data appear to follow a trend pattern.

The data appear to follow a seasonal pattern.

The data appear to follow a cyclical pattern.

The data appear to follow a horizontal pattern.

(b)

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

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

1 | 24 | |

2 | 13 | |

3 | 20 | |

4 | 12 | |

5 | 19 | |

6 | 23 | |

7 | 15 |

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 | 24 | |

2 | 13 | |

3 | 20 | |

4 | 12 | |

5 | 19 | |

6 | 23 | |

7 | 15 |

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 exponential smoothing using *α* = 0.2 provides a
better forecast since it has a smaller 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.

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 larger MSE than the exponential smoothing using *α*
= 0.2.

Answer #1

(a) The time series plot is:

The data appear to follow a horizontal pattern.

(b)

Period | Demand | Forecast | |

Period 1 | 24 | ||

Period 2 | 13 | ||

Period 3 | 20 | ||

Period 4 | 12 | 19 | |

Period 5 | 19 | 15 | |

Period 6 | 23 | 17 | |

Period 7 | 15 | 18 |

MSE = 27.5

The forecast for month 8 = 19

(c)

Period | Demand | Forecast | |

Period 1 | 24 | ||

Period 2 | 13 | 24 | |

Period 3 | 20 | 21.8 | |

Period 4 | 12 | 21.44 | |

Period 5 | 19 | 19.55 | |

Period 6 | 23 | 19.44 | |

Period 7 | 15 | 20.15 |

MSE = 42.15

The forecast for month 8 = 19.12

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

Please give me a thumbs-up if this helps you out. Thank you!

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2
3
4
5
6
7
Value
22
11
18
10
17
21
13
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The data appear to follow a seasonal pattern.
The data appear to follow a trend
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1
2
3
4
5
6
7
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24
13
20
12
19
23
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If required, round your answers to two decimal places. Do not
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2
3
4
5
6
7
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23
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13
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1
2
3
4
5
6
Value
19
12
16
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18
13
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2
12
3
16
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1
2
3
4
5
6
7
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24
13
18
12
18
23
15
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Time Series
Value
Forecast
Forecast
Error
Squared Forecast
Error
1
24
2
13
3
18
4
12
?
?
?
5
18
?
?
?
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1
2
3
4
5
6
Value
18
13
16
11
17
14
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Value
Forecast
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18
2
13
3
16
4
11
_______
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17
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_______
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2
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16
6
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