Question

An additive model of time series with the
components T,S,C&I is?​

Answer 1

Answer:

There is a different kind of forces which influence the time series analysis. Some are continuously effective while others make themselves felt at recurring time intervals. So, our first task is to divide the data and elements into components.

A time series consists of the following four components or basic elements:

Basic or Secular or Long-time trend;

Seasonal variations;

Business cycles or cyclical movement; and

Erratic or Irregular fluctuations.

These components provide a basis for the explanation of the behavior on the past time. With their help, one can predict the behavior ahead. The major tendency of each component or constituent is largely due to causal factors. Additive Model

In the additive model, we represent a particular observation in a time series as the sum of these four components.

i.e. O = T + S + C + I

where O represents the original data, T represents the trend. S represents the seasonal variations, C represents the cyclical variations and I represents the irregular variations.

In another way, we can write Y(t) = T(t) + S(t) +C(t) + I(t)

2) Multiplicative Model

In this model, four components have a multiplicative relationship. So, we represent a particular observation in a time series as the product of these four components:

i.e. O = T × S × C × I

where O, T, S, C and I represents the terms as in additive model.

In another way, we can write Y(t) = T(t) × S(t) × C(t) × I(t)

This model is the most used model in the decomposition of time series. To remove any doubt between the two models, it should be made clear that in Multiplicative model S, C, and I are indices expressed as decimal percentages whereas, in Additive model S, C and I are quantitative deviations about a trend that can be expressed as seasonal, cyclical and irregular in nature.