Question

The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.

Year	1962	1963	1964	1965	1966	1967	1968	1969	1970	1971	1972	1973	1974	1975	1976
Production (Million Barrels)	0	0	1	1	2	3	4	5	6	7	8	9	8	9	10

i. Obtain trend values for the above data using 5-yearly moving averages.
ii. Plot the original time series and trend values obtained above on the same graph.

Answer 1

i.

Year t	Production (millions of barrels) yt	5–yearly moving total	5–yearly moving averages trend value
1962	0	–	–
1963	0	–	–
1964	1	4	0.8
1965	1	7	1.4
1966	2	11	2.2
1967	3	15	3
1968	4	20	4
1969	5	25	5
1970	6	30	6
1971	7	35	7
1972	8	38	7.6
1973	9	41	8.2
1974	8	44	8.8
1975	9	–	–
1976	10	–	–

ii.
Taking year on X-axis and production trend on Y-axis, we plot the points for production corresponding to years to get the graph of time series and plot the points for trend values corresponding to years to get the graph of trend as shown in the adjoining figure. Production: 5 yearly moving Average: ---------------