Question

For the time series below, enter the exponential smoothing predictions, rounded to the nearest 0.01. Let alpha=0.25. Then calculate the error and MSE.

Week	Time Series	Exponential Smoothing	Error
1	8
2	12
3	15
4	11
5	13
6	16

Mean Absolute Error:

Mean Squared Error:

Exp. Smoothed prediction for week 7:

Answer 1

The exponential smoothing forecast is calculated as

F_t+1 = Y_t + ( 1 - ) F_t

The exponential smooting forecast for week 1 = 8

Error = 0

Week 2 = 0.25 * 8 + ( 1 - 0.25) * 8

Week 2 = 8

Error = 4

Week 3 = 0.25 * 12 + (1-0.25)*8

Week 3 = 9

Error = ( 15 - 9) 6

Week 4 = 0.25 * 15 + ( 1-0.25)*9

Week 4 = 11.50

error = (11-11.50) ( -0.5)

week 5 = 0.25 * 11 + (1-0.25)*11.50

week 5 = 11.375

error = 13 - 11.375 ( 1.625)

week 6 = 0.25 * 13 + ( 1-0.25) * 11.375

week 6 = 11.78

errror = ( 16 - 11.78) 4.22

Mean Absolute Error = ( 0+4+6+0.5+1.625+4.22)6

Mean Absolute Error = 2.72

Mean squared error = ( 0+16+36+0.25+2.64+17.8084)6

Mean squared error = 12.12

Exp. Smoothed prediction for week 7 = 0.25 * 16 + ( 1-0.25)*11.78

Exp. Smoothed prediction for week 7 = 12.84

Week	Time Series	Exponential Smoothing	Error	Absolute error	Squared error
1	8	8	0	0	0
2	12	8	4	4	16
3	15	9	6	6	36
4	11	11.5	-0.5	0.5	0.25
5	13	11.375	1.625	1.625	2.640625
6	16	11.78	4.22	4.22	17.8084