Question

Question2:                                                                                         

A manager use his company profit time series for one goods to calculate forecast for upcoming years. He use

F1 = Moving Average Method for 3 years

F2 = Weight Moving Average for 3 years

F3 = Exponential Smoothing Method with α = 0.2

F4 = Exponential Smoothing Method with α = 0.7

His calculation represent in the following table. Gide the manager to chose the better method by calculate MAD and MES for each method

t	y	F1=MA(3)	F2=WMA(3)	F3=exp(0.2)	F4=exp(0.7)
1	58	-	-	-	-
2	46	-	-	58.0	58.0
3	55	-	-	55.6	49.6
4	39	53.0	53.5	55.5	53.4
5	42	46.7	42.9	52.2	43.3
6	63	45.3	42.7	50.1	42.4
7	54	48.0	56.4	52.7	56.8
8	55	53.0	54.6	53.0	54.8
9	61	57.3	55.6	53.4	55.0
10	52	56.7	59.1	54.9	59.2
11	-	56.0	54.1	54.3	54.2

Answer 1

F1:

period	demand	forcast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	58
2	46
3	55
4	39	53.000	-14.00	14.00	196.00
5	42	46.700	-4.70	4.70	22.09
6	63	45.300	17.70	17.70	313.29
7	54	48.000	6.00	6.00	36.00
8	55	53.000	2.00	2.00	4.00
9	61	57.300	3.70	3.70	13.69
10	52	56.700	-4.70	4.70	22.09

MAD/MAE=   Σ |et|/n =    7.54
      
MSE=   Σ(et)²/n =    86.74
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F2:

period	demand	forcast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	58
2	46
3	55
4	39	53.500	-14.50	14.50	210.25
5	42	42.900	-0.90	0.90	0.81
6	63	42.700	20.30	20.30	412.09
7	54	56.400	-2.40	2.40	5.76
8	55	54.600	0.40	0.40	0.16
9	61	55.600	5.40	5.40	29.16
10	52	59.100	-7.10	7.10	50.41

MAD/MAE=   Σ |et|/n =    7.29
      
MSE=   Σ(et)²/n =    101.23

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F3

period	demand	forcast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	58
2	46	58.000	-12.00	12.00	144.00
3	55	55.600	-0.60	0.60	0.36
4	39	55.500	-16.50	16.50	272.25
5	42	52.200	-10.20	10.20	104.04
6	63	50.100	12.90	12.90	166.41
7	54	52.700	1.30	1.30	1.69
8	55	53.000	2.00	2.00	4.00
9	61	53.400	7.60	7.60	57.76
10	52	54.900	-2.90	2.90	8.41

MAD/MAE=   Σ |et|/n =    7.33
      
MSE=   Σ(et)²/n =    84.32

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F4

period	demand	forcast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	58
2	46	58.000	-12.00	12.00	144.00
3	55	49.600	5.40	5.40	29.16
4	39	53.400	-14.40	14.40	207.36
5	42	43.300	-1.30	1.30	1.69
6	63	42.400	20.60	20.60	424.36
7	54	56.800	-2.80	2.80	7.84
8	55	54.800	0.20	0.20	0.04
9	61	55.000	6.00	6.00	36.00
10	52	59.200	-7.20	7.20	51.84

MAD/MAE=   Σ |et|/n =    7.77
      
MSE=   Σ(et)²/n =    100.25

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Hence we can say that F3 is the best method

Please revert back in case of any doubt.

Please upvote. Thanks in advance.