Question

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

Answer 1

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