Consider the following time series data.

Month 1 2 3 4 5 6 7

Value 25 14 21 13 20 24 16

(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 8 to 20 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 8 to 20 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 13 to 25 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 13 to 25 on the vertical axis. The plot reaches its maximum time series value at month 1.

What type of pattern exists in the data?

-The data appear to follow a cyclical pattern.

-The data appear to follow a seasonal pattern.

-The data appear to follow a horizontal pattern.

-The data appear to follow a trend pattern.

(b)

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

Month Time Series
Value Forecast

1 25 ?

2 14 ?

3 21 ?

4 13 ?

5 20 ?

6 24 ?

7 16 ?

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

MSE =??

What is the forecast for month 8???

(c)

Use ? = 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 25 ?

3 21 ?

4 13 ?

5 20 ?

6 24 ?

7 16 ?

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

? = 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 smaller MSE than the exponential smoothing using ? = 0.2.

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

- The exponential smoothing using ? = 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 ? = 0.2.

Question

Consider the following time series data.

Month	1	2	3	4	5	6	7
Value	25	14	21	13	20	24	16

(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 8 to 20 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 8 to 20 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 13 to 25 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 13 to 25 on the vertical axis. The plot reaches its maximum time series value at month 1.

What type of pattern exists in the data?

-The data appear to follow a cyclical pattern.

-The data appear to follow a seasonal pattern.

-The data appear to follow a horizontal pattern.

-The data appear to follow a trend pattern.

(b)

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

Month	Time Series Value	Forecast
1	25	?
2	14	?
3	21	?
4	13	?
5	20	?
6	24	?
7	16	?

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

MSE =??

What is the forecast for month 8???

(c)

Use ? = 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	25	?
3	21	?
4	13	?
5	20	?
6	24	?
7	16	?

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

? = 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 smaller MSE than the exponential smoothing using ? = 0.2.

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

- The exponential smoothing using ? = 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 ? = 0.2.

Accepted Answer

The time series data in the question is as follows:

Month(t)
Value(y)

1
25

2
14

3
21

4
13…