Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	17	12	14	10	16	13

(a) Construct a time series plot.

(b)Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.)

Week	Time Series Value	Forecast
1	17
2	12
3	14
4	10
5	16
6	13

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7?

(c) Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Week	Time Series Value	Forecast
1	17
2	12
3	14
4	10
5	16
6	13

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7? (Round your answer to two decimal places.)

(d) Compare the three-week moving average approach with the exponential smoothing approach using α = 0.2.

Which appears to provide more accurate forecasts based on MSE? Explain.

The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.

The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach.    

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

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

(e) Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.

Week	Time Series Value	Forecast
1	17
2	12
3	14
4	10
5	16
6	13

Answer 1

a)]

b)

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error	MAPE
1	17
2	12
3	14
4	10	14.33	4.33	18.78	0.4333
5	16	12.00	4.00	16.00	0.2500
6	13	13.33	0.33	0.11	0.0256
		Total	8.67	34.89	0.2756
		Average	2.89	11.63	13.78%
			MAD	MSE	MAPE
MSE =			11.63
forecast for week 7 =			13.00

c)

for exponential smoothing: next period forecast =α*last period actual+(1-α)*last period forecast

Time period	Actual Value(A)	Forecast(F)
1	17
2	12	17.00
3	14	16.00
4	10	15.60
5	16	14.48
6	13	14.78

MSE =			13.17
forecast for week 7 =			14.42

d)

The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.

e)

Time period	Actual Value(A)	Forecast(F)
1	17
2	12	17.00
3	14	15.00
4	10	14.60
5	16	12.76
6	13	14.06