Question

Consider the following time series data:

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

Value |
23 | 13 | 21 | 13 | 19 | 21 | 17 |

(a) |
Create a time series plot. |

What type of pattern exists in the data? | |

- Select your answer -Positive trend patternHorizontal patternVertical patternNegative trend patternItem 2 | |

(b) |
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: | |

(c) |
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: | |

(d) |
Compare the three-month moving average forecast with the
exponential smoothing forecast using α = 0.2. Which
appears to provide the better forecast based on MSE? |

- Select your answer -3-month moving averageexponential smoothingItem 7 | |

(e) |
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. |

Answer #1

a)

Horizontal

b)

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

1 | 23 | |||

2 | 13 | |||

3 | 21 | |||

4 | 13 | 19.00 | -6.00 | 36.00 |

5 | 19 | 15.67 | 3.33 | 11.11 |

6 | 21 | 17.67 | 3.33 | 11.11 |

7 | 17 | 17.67 | -0.67 | 0.44 |

total | 58.67 |

MSE=14.67

forecast =19

c)

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

1 | 23 | |||

2 | 13 | 23.00 | -10.00 | 100.00 |

3 | 21 | 21.00 | 0.00 | 0.00 |

4 | 13 | 21.00 | -8.00 | 64.00 |

5 | 19 | 19.40 | -0.40 | 0.16 |

6 | 21 | 19.32 | 1.68 | 2.82 |

7 | 17 | 19.66 | -2.66 | 7.05 |

total | 174.04 |

MSE=29.01

forecast =19.13 (try 19.12 if this comes wrong)

d) three-month moving average forecast o provide the better forecast due to smaller MSE

e)

alpha =0.32

Consider the following time series data:
Month 1 2 3 4 5 6 7
Value 23 13 21 13 19 21 17
b)
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:
(c)
Use α = 0.2 to compute the exponential smoothing
values for the time series. Compute MSE and a forecast...

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Month
1
2
3
4
5
6
7
Value
24
13
20
12
19
23
15
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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:
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Use α = 0.2 to compute the exponential smoothing values
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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
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The data appear to follow a horizontal pattern.
The data appear to follow a cyclical pattern.
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Month
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Value
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1...

Month
1 2 3 4 5 6 7
Value
24 15 21 13 19 21 16
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Week
1
2
3
4
5
6
Value
19
12
16
11
18
13
(b)
Develop the three-week moving average forecasts for this time
series. (Round your answers to two decimal places.)
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Time Series
Value
Forecast
1
19
2
12
3
16
4
11
5
18
6
13
Compute MSE. (Round your answer to two decimal places.)
MSE =
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Use α = 0.2 to compute...

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Month
1
2
3
4
5
6
7
Value
24
13
20
12
19
23
15
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Week 1 2 3 4 5 6
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If required, round your answers to two decimal places.
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If required, round your answers to two decimal places.
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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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2
13
3
16
4
11
_______
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_______
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_______
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Week
1
2
3
4
5
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