Question

Below you are given the first five values of a quarterly time series of sales.

Year	Quarter	Time Series Value Yt
1	1	36
	2	24
	3	16
	4	20
2	1	44

21. Refer to data above. When a naïve method is used, what is the forecast on the sales in Quarter 2 of Year 2.

a. 20 b. 44 c. 27 d. 30

22. Refer to data in Q21. When a three-quarter moving average is used, what is the forecast on the sales in Quarter 2 of Year 2.

a. 20.5 b. 44.3 c. 26.7 d. 30.2

23. Refer to data in Q21. When a three-quarter weighted moving average (W1= 0.5, W2 = 0.3, and W3 = 0.2) is used, what is the forecast on the sales in Quarter 2 of Year 2. (Hint: Ft+1 = W1Dt + W2D ( t – 1) + W3D ( t – 2) )

a. 24.4 b. 30.2 c. 22.8 d. 31.2

24. Refer to data in Q21. When an exponential smoothing model is used with a smoothing parameter alpha of 0.30 and a Q1-Year 2 forecast is 20, what is the forecast on the sales in Quarter 2 of Year 2. (Hint: Ft+1 = aYt + (1 – a)Ft)

a. 27.2 b. 29.2 c. 31.2 d. 33.2

25. Refer to data in Q21. The equation for the trend line of quarterly sales is Ft = 24.4 + 1.2t. What is the forecast on the sales in Quarter 2 of Year 2. (Hint: t=1 for Q1-Year 1, 2 for Q2-year 1, and so on )

a. 31.2 b. 30.4 c. 32.2 d. 31.6

Please show how each answer was obtained. Thank you!

Answer 1

Solution 21:

Option b is correct.

We compute the average sales first.

Average sales = (36 + 24 + 16 + 20)/4 = 24 it is the value that will increase around 24.

From previous trend it shows that value changes occasionally with a margin of 4 units therefore from 1st quarter to 2nd quarter of the following year will earn 24 - 4 = 20 which is adjsuted. Using the formula shows that predicted value for quarter two will be Q2 = 20 + 24 = 44.

Solution 22:

Option c is correct.

Step 1; calculate the mean for the first 3 data = (36+24+16)/3 = 25.33

Step 2; Calculate the mean of the second data set = (24+16+20)/3 =20

Step 3; Calculate the mean of the second data set = (16+20+44)/3= 26.66

Solution 23:

Option a is correct.

Ft+1 = W1Dt + W2D (t – 1) + W3D (t – 2) )

Ft+1 =0.5(25.33) + 0.3(20) +0.2(26.66) = 24.4

Solution 24:

Option a is correct.

Ft+1 = aYt + (1 – a)Ft

Ft+1 = 0.3(44) + (1 – 0.3)20 = 27.2

Solution 25:

Option d is correct.

t=1 for Q1-Year 1, 2 for Q2-year 1, and so on

Therefore q2 year 2 is the 6thperiod

Ft = 24.4 + 1.2t t=6, Q2-Year 2

Ft = 24.4 + 1.2(6) = 31.6