Question

# Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13...

Consider the following time series data.

 Week 1 2 3 4 5 6 Value 18 13 16 11 17 14

A) What type of pattern exists in the data? (HORIZONTAL OR TREND)

B) Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. If required, round your answers to two decimal places.

Week
Time Series
Value

Forecast
1 18
2 13
3 16
4 11 _______
5 17 _______
6 14 _______

MSE: __________
The forecast for week 7: __________

C) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. If required, round your answers to two decimal places.

Week
Time Series
Value

Forecast
1 18
2 13 _______
3 16 _______
4 11 _______
5 17 _______
6 14 _______

MSE: __________
The forecast for week 7: __________

D) Compare the three-week moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE? (THREE WEEK MOVING AVERAGE OR EXPONENTIAL SMOOTHING?). Explain.

E) Use trial and error to find a value of the exponential smoothing coefficient α that results in a smaller MSE than what you calculated for α = 0.2.

CHOICES:

- Any alpha greater than .2 but less than .58 provides better results

- Any alpha less than .2 provides better results

- Any alpha greater than .58 provides better results

- Any alpha less than .2 or greater than .58 provides better results

A)type of pattern: Horizontal

b)

 Time period Actual Value(A) Moving avg. Forecast(F) Forecast error E=|A-F| Squared Forecast Error 1 18 2 13 3 16 4 11 15.67 4.67 21.78 5 17 13.33 3.67 13.44 6 14 14.67 0.67 0.44 Total 9.00 35.67 Average 3.00 11.89 MAD MSE

MSE =11.89

forecast =14

c)

 Time period Actual Value(A) Forecast(F) Forecast error E=A-F Squared Forecast Error 1 18 2 13 18.00 5.00 25.00 3 16 17.00 1.00 1.00 4 11 16.80 5.80 33.64 5 17 15.64 1.36 1.85 6 14 15.91 1.91 3.66 Total 15.07 65.15 Average 3.01 13.03 MAD MSE

MSE =13.03

forecast for week 7 =15.53

d) THREE WEEK MOVING AVERAGE

e)Any alpha greater than .2 but less than .58 provides better results

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