Question

# Consider the following time series data. Month 1 2 3 4 5 6 7 Value 24...

Consider the following time series data.

 Month Value 1 2 3 4 5 6 7 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

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

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.

(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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