Page 302 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 23 : Time Series Methods—Graphic, Method of Semi-averages

3. Although this method seems to be quite simple, in actual practice it is very time-consuming to Notes
construct a freehand trend if a careful and conscientious job is to be done. It is only after long
experience in trend fitting that a person should attempt to fit a trend line by inspection.

To determine the trend values by the semi-average method, the series in question is first
divided into two equal segments; then the arithmetic mean for each part is computed.

23.2 Semi-averages Method

To determine the trend values by the semi-average method, the series in question is first divided into
two equal segments; then the arithmetic mean for each part is computed. Lastly, a straight line passing
through these two averages is drawn to provide the trend for the series. Each average provides the
trend value for the middle time period of the corresponding segment. When the time series includes
an odd number of periods, there are three methods for separating the series :
(a) Add half of the value of the middle period to the total value of each part.
(b) Add the total value of the middle period to the total value of each part.
(c) Drop the value of the middle period from the computations of the averages.
With the semi-average method, the middle time unit is considered as the origin, and the values of the
Y-intercept and the slope of the straight line are derived by applying the following equations :
S + S 2
1
a = t + t 2 ... (1)
1
S − S 1
2
b = tn t 2 ) ... (2)
(
−
1
where t and t refer to the number of time units for the first and second segments in the series; S and
1 2 1
S refer to the corresponding partial sums respectively; and n is the total number of periods in the series.
2
Example 2: For the purpose of example the above method, we shall use the data given in
Table 1. This series contains 15 years and is divided into two parts with 7 years in
each, the middle year being dropped.
Table 1 : Computation of Trend by Semi-average Method for the Data Relating to Number of
Persons Registered in an Employment Exchange in an Indian State During 1965-1979 (Figures
Given in Thousands)
Year X No. of persons Semi-average Trend value

1965 – 7 10.5 11.6
1966 – 6 15.3 12.3
l967 – 5 13.5 12.9
1968 – 4 12.9 13.6 13.6
1969 – 3 11.1 14.3
1970 – 2 15.9 14.9
1971 – 1 16.0 15.6
1972 0 16.5 16.3
1973 1 16.0 17.0
1974 2 16.4 17.6
1975 3 19.9 18.3
1976 4 21.7 19.0 19.0

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