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Method of estimating seasonal indices

The measures of seasonal variations are called seasonal indices which are expressed either in terms of absolute values viz : S = Y – (T + C + I) under the additive model, or in terms of percentages of the remaining components viz : S = TSCI/ TCI × 100, or  Y/TCI × 100 under the multiplicative model. It may be noted that in order to compute the seasonal variations in a time series, the data must be expressed season wise (i.e. month wise, quarters wise or week wise etc.). They cannot be computed from the data given in annual fashion for that they do not exhibit any seasonal variations it them. Thus, for the monthly data, there would be 12 seasonal indices in a year, for the quarterly data 4 seasonal indices in a year and for the weekly data 52 seasonal indices in a year.

Different types of seasonal Index

A seasonal index is mainly of two types:

(i) Specific seasonal index

(ii) Typical seasonal index.

A specific seasonal index is one which is obtained for each part of year i.e. for each month, quarter, or week. These indices are computed as percentage of their periodical average i.e. monthly, quarterly, or weekly averages as the case may be.

A Typical seasonal indexon the other hand, is one which is obtained for a year by averaging a number of specific seasonal indices.

Methods of computation

There are various methods of computing the seasonal variations in a time series. The most important and popular ones among them are the following:

  • Method of Simple average
  • Method of Ration to trend
  • Method of Ratio to moving average
  • Method of Link relatives or Pearson’s method.

Broadly speaking, there are two types of used of seasonal indices which can be made advantageously by a statistician. These are as follows:

  • They can be used analytically to convert the observed data into the deseasonalised data that may help in the study of short-run fluctuations in a series not associated with the seasonal variations. This is done simply by division of the observed data by the corresponding seasonal indices. Thus, TCI =  TSCI/ S
  • They can be used synthetically for business, and economic forecasting, and managerial control as well. The managements, invariably, make use of the seasonal patterns of their business that directly influence their employments, productions, purchases, sales and inventory policies.

Despite the above usefulness in the field of business, economics, and society at large, the seasonal indices suffer from the following limitations for which necessary precautions should be taken in their use.

  • They are computed on the basis of an unrealistic assumption that the seasonal always change in some regular and systematic pattern.
  • They cannot be measured definitely and precisely by any of the methods discussed.
  • They consist of a series of measures each of which usually differs considerably from 100.
  • They may not have any significance for a particular year; through they indicate a pronounced pattern.
  • If the pattern of seasonal variations in a series is not stable, any average pattern may give a poor representation of the actual seasonal variation taking place during the given year.




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