Question

Consider the following time series data: Month 1 2 3 4 5 6 7 Value 24 13 21 14 20 23 15 (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: (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

Answer c: Exponential forecast, alpha 0.2

Month	Demand, At	Forecast, Ft	Absolute deviation= |Forecast - Actual|	squared deviation= (absolute deviation)^2
1	24	24.0
2	13	24.00	11.0	121.0
3	21	21.80	0.8	0.6
4	14	21.64	7.6	58.4
5	20	20.11	0.1	0.0
6	23	20.09	2.9	8.5
7	15	20.67	5.7	32.2
8		19.54
				36.78
				MSE

• the formula to be used in Simple Exponential smoothing is

F_t+1= alpha*A_t + (1-alpha) F_t

A_t means Actual demand of t'th period, if you want to find out the Forecast through exponential smoothing= forecast of 3rd period = alpha*actual demand of 2nd period +(1-alpha) *forecast demand of 2nd period

• remember forecast of 1st period is not given so we will take it as same as the actual= 24, alpha= 0.2

Answer e: Trial and error for bet alpha

Fore alpha= 0.4

Month	Demand, At	Forecast, Ft	Absolute deviation= |Forecast - Actual|	squared deviation= (absolute deviation)^2
1	24	24.0
2	13	24.00	11.0	121.0
3	21	19.60	1.4	2.0
4	14	20.16	6.2	37.9
5	20	17.70	2.3	5.3
6	23	18.62	4.4	19.2
7	15	20.37	5.4	28.8
8		18.22
				35.71
				MSE

Fore alpha= 0.6

Month	Demand, At	Forecast, Ft	Absolute deviation= |Forecast - Actual|	squared deviation= (absolute deviation)^2
1	24	24.0
2	13	24.00	11.0	121.0
3	21	17.40	3.6	13.0
4	14	19.56	5.6	30.9
5	20	16.22	3.8	14.3
6	23	18.49	4.5	20.3
7	15	21.20	6.2	38.4
8		17.48
				39.64
				MSE

For alpha = 0.8

Month	Demand, At	Forecast, Ft	Absolute deviation= |Forecast - Actual|	squared deviation= (absolute deviation)^2
1	24	24.0
2	13	24.00	11.0	121.0
3	21	15.20	5.8	33.6
4	14	19.84	5.8	34.1
5	20	15.17	4.8	23.3
6	23	19.03	4.0	15.7
7	15	22.21	7.2	51.9
8		16.44
				46.63
				MSE

For alpha= 0.3

Month	Demand, At	Forecast, Ft	Absolute deviation= |Forecast - Actual|	squared deviation= (absolute deviation)^2
1	24	24.0
2	13	24.00	11.0	121.0
3	21	20.70	0.3	0.1
4	14	20.79	6.8	46.1
5	20	18.75	1.2	1.6
6	23	19.13	3.9	15.0
7	15	20.29	5.3	28.0
8		18.70
				35.29
				MSE

Alpha= 0.3 is the best as it gives the least value of MSE

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