Question

Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. If required, round your answers to two decimal places. What am i doing wrong in this problem?

Answer 1

According to the given information , if , the exponential smoothing time series is determined as:

0.2

$F_{t}=\alpha T_{t-1}+(1-\alpha )F_{t-1}$

Forecast value of different week are as follows:

$F_{2}=\alpha T_{2-1}+(1-\alpha )F_{2-1}$

  

0.2 × 18 + (1-02) × 18

  

3.6 14.4

  

18

$F_{3}=\alpha T_{3-1}+(1-\alpha )F_{3-1}$

  

0.2 × 13 + (1-02) × 18

  

2.6 + 14.4

  

17

$F_{4}=\alpha T_{4-1}+(1-\alpha )F_{4-1}$

  $=0.2\times 16+(1-0.2)\times 17$

  

3.2+ 13.6

  $=16.8$

$F_{5}=\alpha T_{5-1}+(1-\alpha )F_{5-1}$

  $=0.2\times 11+(1-0.2)\times 16.8$

  $=2.2+13.44$

  $=15.64$

$F_{6}=\alpha T_{6-1}+(1-\alpha )F_{6-1}$

  $=0.2\times 17+(1-0.2)\times 15.64$

  

3.4+ 12.512

  $=15.912$

Therefore forecast value of 7th week is determined as:

$F_{7}=\alpha T_{7-1}+(1-\alpha )F_{7-1}$

  $=0.2\times 14+(1-0.2)\times 15.9120$

  $=2.8+12.7296$

  $=15.5296$

Week	Time Series Value $(T_{t})$	Forecast $(F_{t})$	Error $\left (E \right )$	$\left (E^{2} \right )$
1	18	-
2	13	18	-5	25
3	16	17	-1	1
4	11	16.8	-5.8	33.64
5	17	15.64	1.36	1.8496
6	14	15.912	-1.912	3.655744
7		15.5296		65.14534

Now the mean square error is determined as:

$MSE=\frac{\sum E^{2}}{5}=\frac{65.145344 }{5}=13.02906$

Therefore the

$MSE=13.0291$