Page 233 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 1. Additive Model: This model is based on the assumption that the value of the variable of a
time series, at a point of time t, is the sum of the four components. Using symbols, we can
write
Y = T + S + C + R , where T , S , C and R are the values of trend, seasonal, cyclical and
t t t t t t t t t
random components respectively, at a point of time t.
This model assumes that all the four components of time series act independently of one
another. This assumption implies that one component has no effect on the other(s)
irrespective of their magnitudes.
2. Multiplicative Model: This model assumes that Y is given by the multiplication of various
t
components. Symbolically, we can write
Y = T × S × C × R
t t t t t
This model implies that although the four components may be due to different causes,
these are, strictly speaking, not independent of each other. For example, the seasonal
component may be some percentage of trend. Similarly, we can have other components
expressed in terms of certain percentage.

There is, in fact, very little agreement amongst the experts about the validity of the
models assumed above. It is not very certain that the components combine themselves in
the manner mentioned in the two models. Consequently, various mixed type of models
have also been suggested, such as
Y = T .S .C + R
t t t t t
or Y = T .C + S .R or Y = T + C .S .R , etc.
t t t t t t t t t t
Out of all the models, given above, the additive and the multiplicative models are often
used. The two models, when applied to the same data, would give different answers.
Though, the additive model may be appropriate in some of the situations, yet it is the
multiplicative model which characterises the majority of the time series in economic and
business fields.

11.1.4 Method of Averages

1. Method of Selected Points: In this method, two points, considered to be the most
representative or normal, are joined by a straight line to get secular trend. This, again, is
a subjective method since different persons may have different opinions regarding the
representative points. Further, only linear trend can be determined by this method.

Example: Determine the trend of the following time series data by the method of selected
points:
Years : 2001 02 2002 03 2003 04 2004 05 2005 06
Per Capita availability
: 521 511 462 525 518
of Tea (gms)
Years : 2006 07 2007 08 2008 09 2009 10
Per Capita availability
: 575 589 546 593
of Tea (gms)

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