# The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.i. Obtain trend values for the above data using 5-yearly moving averages. ii. Plot the original time series - Mathematics and Statistics

Sum

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) 10 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.

#### Solution

i.

 Year t Production (millions of barrels) yt 5–yearly moving total 5–yearly moving averages trend value 192 10 – – 1963 0 – – 1964 1 14 2.8 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: ---------------

Concept: Measurement of Secular Trend
Is there an error in this question or solution?
Chapter 4: Time Series - Exercise 4.1 [Page 67]

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