Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	13	17	12	17	15

a. develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary).

b. use = 0.2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7 (to 2 decimals).

c. use a smoothing constant of =0.4 to compute the MSE (to 2 decimals).

Answer 1

a)

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	18
2	13
3	17
4	12	16.00	4.00	16.00
5	17	14.00	3.00	9.00
6	15	15.33	0.33	0.11
		Total	7.33	25.11
		Average	2.44	8.37
			MAD	MSE
MSE =			8.37
forecast for week 7 =			14.67

b)

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

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	17	17.00	0.00	0.00
4	12	17.00	5.00	25.00
5	17	16.00	1.00	1.00
6	15	16.20	1.20	1.44
		Total	12.20	52.44
		Average	2.44	10.49
			MAD	MSE
MSE =			10.49
forecast for week 7 =			15.96

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	17	16.00	1.00	1.00
4	12	16.40	4.40	19.36
5	17	14.64	2.36	5.57
6	15	15.58	0.58	0.34
		Total	13.34	51.27
		Average	2.67	10.25
			MAD	MSE
MSE =			10.25