Question

Following are time-series data for ten different periods. Use exponential smoothing to forecast the values for periods 3 through 10. Use the value for the first period as the forecast for the second period. Compute forecasts using α = 0.8. Compute the MAD and MSE.

Time period	Value
1	27
2	31
3	58
4	63
5	59
6	66
7	71
8	86
9	101
10	97

Group of answer choices

a) MAD=9.7, MSE=1585.6

b) MAD=9.7, MSE=176.2

c) MAD=10.2, MSE=1585.6

d) MAD=10.2, MSE=176.2

Answer 1

Time period	Value	Forecast	Error	Error^2	|Error|
1	27
2	31	27	4	16	4
3	58	30.2	27.8	772.84	27.8
4	63	52.44	10.56	111.5136	10.56
5	59	60.888	-1.888	3.564544	1.888
6	66	59.3776	6.6224	43.85618	6.6224
7	71	64.67552	6.32448	39.99905	6.32448
8	86	69.7351	16.2649	264.5468	16.2649
9	101	82.74702	18.25298	333.1712	18.25298
10	97	97.3494	-0.3494	0.122083	0.3494
α =	0.8
			MSE=	1585.6
			MAD=		10.2

Forecast is calculated using;

MSE=sum of suqare of error

MAD=Average of absolute sum of error.

We get:

MSE=1585.6

MAD=10.2

Hence,option (C) MAD=10.2, MSE=1585.6 is correct .

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