(a) right choice is first.
there is seasonality pattern in the data ( please give the options for appropriate answer)
(b)
t | yt | Forecast | forecast error | squared forecast error | |
1 | 21 | ||||
2 | 14 | ||||
3 | 18 | ||||
4 | 13 | 17.6667 | -4.6667 | 21.7778 | |
5 | 18 | 15.0000 | 3.0000 | 9.0000 | |
6 | 21 | 16.3333 | 4.6667 | 21.7778 | |
7 | 14 | 17.3333 | -3.3333 | 11.1111 | |
total | 63.6667 |
MSE=SQRT(63.6667/4)=3.9896
forecast for month 8=(18+21+14)/3=17.6667
(c)
alpha= | 0.2 | ||||
t | Yt | Ft=alpha*Y(t-1)+(1-alpha)*F(t-1) | forecast error | squared forecast error | |
1 | 21 | ||||
2 | 14 | 21.0000 | -7.0000 | 49.0000 | |
3 | 18 | 19.6000 | -1.6000 | 2.5600 | |
4 | 13 | 19.2800 | -6.2800 | 39.4384 | |
5 | 18 | 18.0240 | -0.0240 | 0.0006 | |
6 | 21 | 18.0192 | 2.9808 | 8.8852 | |
7 | 14 | 18.6154 | -4.6154 | 21.3015 | |
8 | 17.6923 | total= | 121.1857 | ||
9 | MSE= | 4.4942 |
MSE=sqrt(121.1857/6)=4.4942
forecast for the month 8=17.6923
(d) right choice is first.
since the 3-months moving average MSE is less than exponential smoothing (alpha=0.2 )
(e) alpha=0.4 is better ( than alpha=0.2).
alpha= | 0.4 | ||||
t | Yt | Ft=alpha*Y(t-1)+(1-alpha)*F(t-1) | forecast error | squared forecast error | |
1 | 21 | ||||
2 | 14 | 21.0000 | -7.0000 | 49.0000 | |
3 | 18 | 18.2000 | -0.2000 | 0.0400 | |
4 | 13 | 18.1200 | -5.1200 | 26.2144 | |
5 | 18 | 16.0720 | 1.9280 | 3.7172 | |
6 | 21 | 16.8432 | 4.1568 | 17.2790 | |
7 | 14 | 18.5059 | -4.5059 | 20.3033 | |
8 | 16.7036 | total= | 116.5539 | ||
9 | MSE= | 4.4075 |
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