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.    

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