Page 221 - DMGT404 RESEARCH_METHODOLOGY

Unit 10: Time Series

Notes
Graphical presentation of Y and T values

Example: Assuming a four-yearly cycle, find the trend values for the following data by
the method of moving average.
Year 1979 1980 1981 1982 1983 1984 1985
Sales (in Rs ‘000) 74 100 97 87 90 115 126
Year 1986 1987 1988 1989 1990 1991 1992
Sales (in Rs ‘000) 108 100 125 118 113 122 126

Solution:
Calculation of Trend Values
Years Scale 4 - Year Moving Centered 4 - Year Moving
(Y) Total Total Average (T)
... ... ...
1979 74 ... ... ...
1980 100 358 732
1981 97 374 763 91.50
95.38
1982 87 389 807 100.88
1983 90 418 857 107.13
1984 115 439 888 111.00
1985 126 449 908 113.50
910
1986 108 459 907 113.75
1987 100 451 934
1988 125 456 957 113.38
1989 118 478 ... 116.75
...
...
1990 113 479 119.63
...
...
1991 122 ...
1992 126
10.3.2 Exponential Smoothing
Exponential smoothing gives greater weight to demand in more recent periods, and less weight
to demand in earlier periods average: At = a Dt + (1 – a) At–1 = a Dt + (1 – a) Ft
forecast for period t + 1: Ft + 1 = At
where:
At –1 = “series average” calculated by the exponential smoothing model to period t – 1

a = smoothing parameter between 0 and 1 the larger the smoothing parameter, the greater
the weight given to the most recent demand

LOVELY PROFESSIONAL UNIVERSITY 215