Page 199 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes By selecting a suitable origin, i.e., defining X = t - origin, such that SX = 0, the computation work
logY X logY
can be simplified. The values of A and B are given by A and B 2
n X
respectively. Thus, the fitted trend equation can be written as log Y = A + BX

or Y = Antilog [A + BX] = Antilog [log a + X log b]
= Antilog [log a.b ] = a.b .
X
X

Notes Merits and Demerits of Least Squares Method
Merits

1. Given the mathematical form of the trend to be fitted, the least squares method is an
objective method.
2. Unlike the moving average method, it is possible to compute trend values for all the
periods and predict the value for a period lying outside the observed data.
3. The results of the method of least squares are most satisfactory because the fitted
trend satisfies the two important properties, i.e., (i) (Y – Y ) = 0 and (ii) (Y – Y ) 2
o t o t
is minimum. Here Yo denotes the observed value and Yt denotes the calculated
trend value.
The first property implies that the position of fitted trend equation is such that the
sum of deviations of observations above and below this is equal to zero. The second
property implies that the sum of squares of deviations of observations, about the
trend equation, are minimum.
Demerits

1. As compared with the moving average method, it is a cumbersome method.
2. It is not flexible like the moving average method. If some observations are added,
then the entire calculations are to be done once again.

3. It can predict or estimate values only in the immediate future or past.
4. The computation of trend values, on the basis of this method, doesn’t take into
account the other components of a time series and hence not reliable.

5. Since the choice of a particular trend is arbitrary, the method is not, strictly, objective.
6. This method cannot be used to fit growth curves, the pattern followed by the most
of the economic and business time series.

Task Study various methods used for fitting of trends and analyze them.

Self Assessment

State whether the following statements are true or false:

11. Least square root method is one of the most popular methods of fitting a mathematical
trend.

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