# DECOMPOSITION OF TIME SERIES

Decomposition and analysis of a time series are one and the same thing.  The original data or observed data ‘O’ is the result of the effects generated by the long-term and short-term causes, namely (1) Trend = T, (2) cyclical – C, (3) Seasonal = S, and (4) Irregular = I.  Finding out the values for each of the components is called decomposition of a time series.  Decomposition is done either by the additive model or the multiplicative model of analysis.  Which of these two models is to be used in analysis of time series depends on the assumption that we might make about the nature and relationship among the four components.

Additive Model: It is based on the assumption that the four components are independent on one another.  Under this assumption, the pattern of occurrence and the magnitude of movements in any particular component are not affect4ed by the other components.  In this model the values of the four components are expressed in the original units of measurement. Thus, the original data or observed data ‘Y’ is the total of the four component values, that is,

Y = T + S + C + I

where, T, S, C and I represents the trend variations, seasonal variations cyclical variations, and erratic variations, respectively.

Multiplicative Model: It is based on the assumption that the causes giving rise to the four components are interdependent.  Thus, the original data or observed data ‘Y’ is the product of four component values, that is:

Y = T × S × C × I

In this model the values of all the components, except trend values, are expressed as percentages.

In business research, normally the multiplicative model is more suited and used more frequently for the purposes of analysis to time series.  Because, the data related to business and economic time series is the result of interaction of a number of factors which individually cannot be held responsible for generating any specific type of variations.