Page 325 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes the trend of the time series is clearly not linear and in which we are concerned only with the general
movements of the time series, whether it is a trend or a cycle or both, it is customary to study the
smoothing behaviour of the series by the use of moving average. Secondly, the characteristic of a
moving average is the basis of seasonal analysis, which shall be discussed in a subsequent section.
Selections of Period in Moving Average Method
The most important point in the average method is the selection of period. The selection of period
depends upon the periodicity of data. The period of moving average method can be divided into two
parts :
(A) Odd Period of Moving Average : Odd period is the period of three, five, seven, nine years and
so on. In case of odd period moving average, no difficulty is faced while placing the computed
average. The determination of trend in odd period moving average can be made clear with the
help of following example :
Example 2 : Calculate trend values by 3-yearly moving average from the following data :

Year : 1980 1981 1982 1983 1984 1985 1986
Sales (‘000 Units) : 5 7 9 12 11 10 8

Solution :

Years Sales (000’ Units) 3-yearly totals 3-yearly moving average
1980 5 — —
1981 7 21 21/3 = 7.00
1982 9 28 28/3 = 9.33
1983 12 32 32/3 = 10.67
1984 11 33 33/3 = 11.00
1985 10 29 29/3 = 9.67
1986 8 — —

The trend value is shown in Figure 2.
Y
14

12
Original Data
10
Trends
Sales (000’ units) 6 4
Line
8

2
0 X
1980 1981 1982 1983 1984 1985 1986
YEAR
Figure 2 :
(B) Even Period of Moving Average : The procedure of calculation of moving average of even
number of years, say, four, six, eight, and so on, is different from the procedure of odd number
of years. Suppose moving average is to be calculated for four years. We will take the total of

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