Question

Consider the following time series data.

Week 1 2 3 4 5 6

Value 18 13 15 13 15 15

(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.

(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.

(d) 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 = 0.20. Use a two-decimal digit precision.

Answer 1

b)

		3 week
Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	18
2	13
3	15
4	13	15.33	2.33	5.44
5	15	13.67	1.33	1.78
6	15	14.33	0.67	0.44
		Total	4.33	7.67
		Average	1.44	2.56
			MAD	MSE

MSE =2.56

forecast =14.33
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	15	17.00	2.00	4.00
4	13	16.60	3.60	12.96
5	15	15.88	0.88	0.77
6	15	15.70	0.70	0.50
		Total	12.18	43.23
		Average	2.44	8.65
			MAD	MSE

MSE =8.65

forecast =15.56

d)value of alpha =0.62