Page 291 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Seasonal indices have been corrected as follows:

+ 100.0 87.45 89.6 96.55
+
+
Average of chain relatives =
4
= 93.4
Corrected chain relative
Corrected seasonal index = × 100
93.4

The other alternative method for determining the seasonal indices is the ratios-to-trend method. This
method assumes that seasonal variation for a given season is a constant fraction of the trend. With
the basic multiplicative model, O = TSCI, it is argued that the trend can be eliminated by dividing
each observation by its corresponding trend value. The ratios resulting from this computation compose
SCI. Each of these ratios to trend is a one-based relative, that is pure number with a unity base. Next,
an average is computed for each season. This averaging process eliminates cyclical and random
(irregular) fluctuations from the ratios to trend. Thus, these averages of ratios to trend contain only
the seasonal component. These averages, therefore, constitute the seasonal indices. However, slight
corrections can be incorporated in order to adjust these ratios to average to unity.
A simplest but a crude method of computing a seasonal index is to calculate the average value for
each season, and express the averages as percentages so that all the seasonal percentages can add up
to 100 multiplied by the number of seasons.
The seasonal indices are used to remove the seasonal effects from a time series. Before identifying
either the trend or cyclical components of a time series, one must eliminate the seasonal variation. To
do this, we divide each of the actual values in the series by the appropriate seasonal index. Once the
seasonal effect has been eliminated, the deseasonalized values that remain in the series reflect only
the trend, cyclical, and irregular components of the time series. With the help of the deseasonalized
values we can project the future.

Uses of Seasonal Variations
The following are the main uses of seasonal variations:

(a) Knowledge of the Pattern of Change: A study of the seasonal variations helps in determining
the pattern of the change. It can be known whether the change is stable or gradual or abrupt.
(b) Helps in the Study of Cyclical Fluctuations: The cyclical and irregular variations can be
accurately studied only after eliminating seasonal components from a time series.
(c) Aid of Policy Decisions: The seasonal variations aid in formulating policy decisions. These are
also useful in planning future variations. For example, the manufacturer may decide to cut the
prices during slack season and providing incentives in the off-season. They may also incur
huge expenditure in advertising off-seasonal use of the product.
(d) Knowledge of the Nature of Change: The study of seasonal variations provides a better
understanding of the nature of variations. For example, in the absence of the knowledge of
seasonal variations a seasonal upswing may be mistaken as an indication of better business
conditions. Similarly, a seasonal slump may be mistaken as an indication of deterioration in
business conditions. While in fact both these changes are seasonal and not of permanent nature.

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