Question

QUESTION 4 [27 marks] Suppose the following quarterly earnings (in N$ millions) have been recorded by Namibia breweries company for the years 2007 to 2010. Year Quarter 2007 2008 2009 2010 1 52 57 60 66 2 67 90 77 82 3 27 75 84 98 4 45 71 63 76 4.1 Compute the 4-period centred moving average for the quarterly sales. [4] 4.2 Compute the seasonal indexes for these quarterly earnings. [10] 4.3 Use the method of least squares from regression analysis to determine the trend line of best fit. Use the zero-sum method for coding. [10] 4.4 Using the trend line you produced in 4.3, estimate the trend value of the time series for Quarter 3 in 2014. [3]

Answer 1

4.1 Compute the 4-period centred moving average for the quarterly sales. [4]

Centered
Moving
Average
48.375
51.875
60.750
70.000
73.625
72.375
71.875
72.000
71.750
73.125
75.500
78.875

4.2 Compute the seasonal indexes for these quarterly earnings. [10]

Seasonal

Indexes

0.921

1.181

0.956

0.943

4.3 Use the method of least squares from regression analysis to determine the trend line of best fit. Use the zero-sum method for coding. [10]

y = 2.4547x + 47.291

4.4 Using the trend line you produced in 4.3, estimate the trend value of the time series for Quarter 3 in 2014. [3]

y = 2.4547*31 + 47.291 = 123.3867

The calculations are:

				Centered
				Moving	Ratio to	Seasonal	Data
t	Year	Quarter	Data	Average	CMA	Indexes	Deseasonalized
1	1	1	52			0.921	56.5
2	1	2	67			1.181	56.7
3	1	3	27	48.375	0.558	0.956	28.3
4	1	4	45	51.875	0.867	0.943	47.7
5	2	1	57	60.750	0.938	0.921	61.9
6	2	2	90	70.000	1.286	1.181	76.2
7	2	3	75	73.625	1.019	0.956	78.5
8	2	4	71	72.375	0.981	0.943	75.3
9	3	1	60	71.875	0.835	0.921	65.2
10	3	2	77	72.000	1.069	1.181	65.2
11	3	3	84	71.750	1.171	0.956	87.9
12	3	4	63	73.125	0.862	0.943	66.8
13	4	1	66	75.500	0.874	0.921	71.7
14	4	2	82	78.875	1.040	1.181	69.4
15	4	3	98			0.956	102.5
16	4	4	76			0.943	80.6