Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	24	13	20	12	19	23	15

	Develop a three-month moving average for this time series. Compute MSE and a forecast for month 8.
	If required, round your answers to two decimal places. Do not round intermediate calculation.
	MSE:
	The forecast for month 8:
(c)	Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8.
	If required, round your answers to two decimal places. Do not round intermediate calculation.
	MSE:
	The forecast for month 8:
(d)	Compare the three-month moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE?

(e)	Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE.
	If required, round your answer to two decimal places.
	α =

Answer 1

b)

for 3 month forecast:

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	24
2	13
3	20
4	12	19.00	7.00	49.00
5	19	15.00	4.00	16.00
6	23	17.00	6.00	36.00
7	15	18.00	3.00	9.00
		Total	20.00	110.00
		Average	5.00	27.50
			MAD	MSE

MSE: =27.50

forecast for month 8=19

c)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	24
2	13	24.00	11.00	121.00
3	20	21.80	1.80	3.24
4	12	21.44	9.44	89.11
5	19	19.55	0.55	0.30
6	23	19.44	3.56	12.66
7	15	20.15	5.15	26.56
		19.12	31.50	252.88
		Average	5.25	42.1461
			MAD	MSE

MSE:=42.15

forecast for month 8 =19.12

d)

three-month moving average forecast

e)

α = 0.35