Page 220 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes Let Y , Y , ...... Yn be the n values of a time series for successive time periods 1, 2, ...... n respectively.
1 2
The calculation of 3-period and 4-period moving averages are shown in the following tables:

It should be noted that, in case of 3-period moving average, it is not possible to get the moving
averages for the first and the last periods. Similarly, the larger is the period of moving average
the more information will be lost at the ends of a time series.
When the period of moving average is even, the computed average will correspond to the
middle of the two middle most periods. These values should be centred by taking arithmetic
mean of the two successive averages. The computation of moving average in such a case is also
illustrated in the above table.

Year : 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
Production
: 26 27 28 30 29 27 30 31 32 31
('000' tonnes)

Example: Determine the trend values of the following data by using 3-year moving
average. Also find short-term fluctuations for various years, assuming additive model. Plot the
original and the trend values on the same graph.
Solution:

Calculation of Trend and Short-term Fluctuations

Production 3-Year Moving 3-Year M . . or Short -term fluctuations
A
Years
T
T
( ) Total Trend values ( ) (Y  )
Y
1981 26   
1982 27 81 27.00 0.00
1983 28 85 28.33  0.33
1984 30 87 29.00 1.00
1985 29 86 28.67 0.33
1986 27 86 28.67  1.67
1987 30 88 29.33 0.67
1988 31 93 31.00 0.00
1989 32 94 31.33 0.67
1990 31   

214 LOVELY PROFESSIONAL UNIVERSITY