Question

The following time series shows the sales of a particular product over the past 12 months. If required, round your answer to two decimal places.

Click on the datafile logo to reference the data.

Month	Sales	Month	Sales
1	105	7	145
2	135	8	140
3	120	9	100
4	105	10	80
5	90	11	100
6	120	12	110

(a)

Choose the correct time series plot.

(i)
(ii)
(iii)
(iv)

- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1

What type of pattern "significantly" exists in the data? (Use 1% level of significance when needed)

- Select your answer -Only randomnessRandomness & Linear trendRandomness & SeasonalityRandomness, Linear trend & SeasonalityItem 2

(b)

Use α = 0.3 to compute the exponential smoothing values for the time series.

Month	Sales	Exp. Sm.
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

(c)

Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE. Enter the best value of alpha to two decimal places.

α =

Answer 1

a)

b)

	α=	0.3
period	demand	forecast
t	Dt	Ft
1	105
2	135	105
3	120	114
4	105	115.8
5	90	112.56
6	120	105.792
7	145	110.0544
8	140	120.53808
9	100	126.376656
10	80	118.463659
11	100	106.924561
12	110	104.847193

d)

Exponential Smoothing
alpha	0.033
data	forecast
105	105
135	105
120	105.9769
105	106.4336
90	106.3869
120	105.8533
145	106.314
140	107.5737
100	108.6297
80	108.3487
100	107.4255
110	107.1837
>	107.2754
MAE	MSE	MAPE
17.6657	459.6929	0.153785

α=0.033