Question

# Consider the following time series data. Month 1 2 3 4 5 6 7 Value 22...

Consider the following time series data.

 Month Value 1 2 3 4 5 6 7 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 pattern.

The data appear to follow a horizontal pattern.

The data appear to follow a cyclical pattern.

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

Month Time Series
Value
Forecast
1 22
2 11
3 18
4 10 ____
5 17 ____
6 21 ____
7 13 ____

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 22
2 11 ____
3 18 ____
4 10 ____
5 17 ____
6 21 ____
7 13 ____

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

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

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 smaller MSE than the exponential smoothing using α = 0.2.

The data appear to follow a horizontal pattern.

b)

 month value forecast |error| error^2 1 22 2 11 3 18 4 10 17.00 -7.00 49.00 5 17 13.00 4.00 16.00 6 21 15.00 6.00 36.00 7 13 16.00 -3.00 9.00 total 110.00 average 27.50 MSE= 27.50 Forecast= 17.00

c)

 month value forecast error error^2 1 22 2 11 22.00 -11.00 121.00 3 18 19.80 -1.80 3.24 4 10 19.44 -9.44 89.11 5 17 17.55 -0.55 0.30 6 21 17.44 3.56 12.66 7 13 18.15 -5.15 26.56 total 252.88 average 42.15 MSE= 42.15 Forecast= 17.12

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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