Trend Ratio Method

This method of calculating a seasonal index also termed as the percent age to trend method, is relatively simple and yet an improvement over the method of simple averages. These methods suppose that the seasonal variation for a given month is constant fraction of trend. The ratio-to-trend method presumably isolated the seasonal factor in the following manner. The Trend is removed when the rations are computed in effect.

T x S x C x I/T = S x C x I.

Random elements are supposed to vanish when the ratios are averaged. A careful selection of the period of years used in the computation is expected to cause the influences or depression to offset each other and thus eliminate the cycle for series which are not subject to pronounced cyclical or random influences and for that trend can be computed accurately. The steps in the computation of seasonal index are:

1. Trend values are first obtained by applying the method of least squares.

2. The next step is to divide the original data month by month by the corresponding trend value & multiply these ratios by 100. The values so obtained are now free from trend and the problem that remains is to free them from irregular and cyclical movements.

3. In order to free the values form irregular and cyclical movements the figures given for different years for January, February, etc, are averaged with any one of the usual measures of central value, for illustrate the median or the mean. If the data are examined month by month, it is sometimes possible to describe a definite cause to usually high or low values. When such causes are found to be associated with irregular variations (like extremely bad weather and earthquake famine etc.) they may be cast out and the mean of the remaining items is known to as a modified mean. Since such scrutiny of the data needs considerable knowledge of prevailing conditions and is to a large extend subjective, it is frequently desirable to use to median which is normally not affected by very high or very low values.

4. The seasonal index for every month is expressed as a percentage of the average month. The sum of 12 values must equal to 1,200 or 100 per cent. If it is not, an adjustment is made by multiplying every index by a suitable factor (1,200 / the sum of the 12 values) this gives the final seasonal index.

Illustration:

Find seasonal variations by the ratio-to- trend method from the data given below:

Solution:

For determining seasonal variation by ratio- to -trend method first we will determine the trend for yearly data and then convert it to quarterly data.

Calculating trend by method of least squares

The equation of the straight line trends is Y = a + b X.

A = Σ Y / N = 280 / 5 = 56 b = Σ XY / Σ X² = 120 / 10 =12

Quarterly increment = 12/4 = 3.