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
Production (million barrels)	0	0	1	1	2	3	4	5
Year	1970	1971	1972	1973	1974	1975	1976
Production (million barrels)	6	7	8	9	8	9	10

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

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

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

Obtain trend values for the above using 5-yearly moving averages:

Answer 1

a. We construct the following table to obtain 5-yearly moving average:

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	3.0
1968	4	20	4.0
1969	5	25	5.0
1970	6	30	6.0
1971	7	35	7.0
1972	8	38	7.6
1973	9	41	8.2
1974	8	44	8.8
1975	9	–	–
1976	10	–	–

b. Taking the year on the X-axis and the production trend on the Y-axis, we plot the points for production corresponding to years to get the graph of the time series and plot the point for trend values corresponding to years to get the graph of the trend as shown below: