Question

Month
1					37
2					44
3					35
4					50
5					34
6					30
7					50
8					29
9					36
10					35
11					41
12					45

a.  Show the naive forecast, an exponential smoothing forecasts using α = 0.2, and a 3-month moving average forecast.

b. Compare the MFE, MSE, and MAPE on the models

c.  Make a conclusion on which model to use.

d. Find the alpha (smoothing constant) that minimizes the MSE.

Answer 1

a)

exponential smoothing α=0.2

period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error	Abs %error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²	| et/Dt |
1	37
2	44	37	7.00	7.00	49.00	15.91%
3	35	38.4	-3.40	3.40	11.56	9.71%
4	50	37.72	12.28	12.28	150.80	24.56%
5	34	40.176	-6.18	6.18	38.14	18.16%
6	30	38.9408	-8.94	8.94	79.94	29.80%
7	50	37.15264	12.85	12.85	165.05	25.69%
8	29	39.722112	-10.72	10.72	114.96	36.97%
9	36	37.5776896	-1.58	1.58	2.49	4.38%
10	35	37.2621517	-2.26	2.26	5.12	6.46%
11	41	36.8097213	4.19	4.19	17.56	10.22%
12	45	37.6477771	7.35	7.35	54.06	16.34%

MFE=   Σet/n =    0.96

MSE=   Σ(et)²/n =    62.61
      
MAPE=   Σ | et/Dt |/n =    18.02%
==============================

naive forecast

period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error	Abs %error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²	| et/Dt |
1	37
2	44	37	7.00	7.00	49.00	15.91%
3	35	44	-9.00	9.00	81.00	25.71%
4	50	35	15.00	15.00	225.00	30.00%
5	34	50	-16.00	16.00	256.00	47.06%
6	30	34	-4.00	4.00	16.00	13.33%
7	50	30	20.00	20.00	400.00	40.00%
8	29	50	-21.00	21.00	441.00	72.41%
9	36	29	7.00	7.00	49.00	19.44%
10	35	36	-1.00	1.00	1.00	2.86%
11	41	35	6.00	6.00	36.00	14.63%
12	45	41	4.00	4.00	16.00	8.89%

MFE=   Σet/n =    0.73
  
MSE=   Σ(et)²/n =    142.73
      
MAPE=   Σ | et/Dt |/n =    26.39%
=====================

3 month moving average-

period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error	Abs %error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²	| et/Dt |
1	37
2	44
3	35
4	50	38.6666667	11.33	11.33	128.44	22.67%
5	34	43	-9.00	9.00	81.00	26.47%
6	30	39.6666667	-9.67	9.67	93.44	32.22%
7	50	38	12.00	12.00	144.00	24.00%
8	29	38	-9.00	9.00	81.00	31.03%
9	36	36.3333333	-0.33	0.33	0.11	0.93%
10	35	38.3333333	-3.33	3.33	11.11	9.52%
11	41	33.3333333	7.67	7.67	58.78	18.70%
12	45	37.3333333	7.67	7.67	58.78	17.04%

MFE=   Σet/n =    0.81

MSE=   Σ(et)²/n =    72.96
      
MAPE=   Σ | et/Dt |/n =    20.29%

b)

MSE is smallest for using exponential smooting

MFE is smallest using naive method

MAPE is smallest for exponential method

c) exponential smooting method should be use

d)

alpha (smoothing constant) = 0.10  minimizes the MSE.