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 = 0.1. 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=296.6, MSE=1266.5

B) MAD=296.6 , MSE=11398.5

C) MAD=32.9, MSE=1266.5

D) MAD=32.9, MSE=11398.5

Answer 1

for exponential smoothing: next period forecast =α*last period actual+(1-α)*last period forecast

period	value	forecast	error	error^2
1	27
2	31	27.00	4.000	16.000
3	58	27.40	30.600	936.360
4	63	30.46	32.540	1058.852
5	59	33.71	25.286	639.382
6	66	36.24	29.757	885.503
7	71	39.22	31.782	1010.074
8	86	42.40	43.603	1901.265
9	101	46.76	54.243	2942.319
10	97	52.18	44.819	2008.728
11		56.66
		average	32.9	1266.5
			MAE	MSE

option C is correct :MAD =32.9   ; MSE =1266.5