Chapter: Time Series· Mathematics & Statistics (Commerce) Part 2

The following table shows the index of industrial production for the period from 1976 to 1985, using the year 1976 as the base year. Obtain the trend values for the following data using 4 yearly centered moving averages :Years197619771978197919801981…

Q.5 (A)(iii) The following table shows the index of industrial production for the period from 1976 to 1985, using the year 1976 as the base year. Obtain the trend values for the following data using 4 yearly centered moving averages :

Years	1976	1977	1978	1979	1980	1981	1982	1983	1984	1985
Index	0	2	3	3	2	4	5	6	7	10

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Answer: Trend values 1978 to 1983 are 2.25, 2.75, 3.25, 3.875, 4.875 and 6.25.

Year	Index	4-yearly moving total	Sum of two consecutive totals (centred)	Trend value (centred total ÷ 8)
1976	0
1977	2
		8
1978	3		18	2.25
		10
1979	3		22	2.75
		12
1980	2		26	3.25
		14
1981	4		31	3.875
		17
1982	5		39	4.875
		22
1983	6		50	6.25
		28
1984	7
1985	10

The 4-yearly totals (0+2+3+3 = 8, 2+3+3+2 = 10, and so on) fall between years, so consecutive totals are added in pairs to centre them on a year, and divided by 8. No trend values are available for the first two and the last two years.

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The following table shows the index of industrial production for the period from 1976 to 1985, using the year 1976 as the base year. Obtain the trend values for the following data using 4 yearly centered moving averages :Years197619771978197919801981…

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